On the Pine Ridge Indian Reservation in South Dakota, extreme weather and bad roads have left some residents stranded for nearly two weeks with limited food and water.

David Gibbons, left, and Shane Mesteth ride down a muddy road to the highway to gather food, water and medical supplies for residents on the Pine Ridge Indian Reservation in South Dakota.

Ella Red Cloud-Yellow Horse, marooned for days by a blizzard and then a flood, needed to get out. Supplies at her house were running low. She had come down with pneumonia. She had a chemotherapy appointment to keep.

But her long driveway was blocked by mountains of mud — impassable even for an ambulance or a tractor.

So Ms. Red Cloud-Yellow Horse, 59, set off toward the road on foot. She fell repeatedly, almost got swept away in the current of a creek, and became stuck in the mud. Finally, more than an hour later, she made it the half-mile to the highway where she was picked up.

“I couldn’t breathe,” she said, “but I knew I needed to get to the hospital.”

Such stories are startlingly common these days on the Pine Ridge Indian Reservation in South Dakota — a stunning stretch of land larger than Delaware — as an overwhelming bout of snow and flooding has set off a humanitarian disaster that seems unlikely to abate soon.

With some residents approaching two weeks stranded in their homes, and with emergency rations able to reach parts of the back country only by horse, boat and helicopter, Pine Ridge remains in a state of shock and triage.

The rising floodwaters stopped just sort of the home where Henry Red Cloud and his family rode out the storm, but other buildings on their property including their solar power business were inundated.

Officials with the Oglala Sioux Tribe, which administers the reservation, say they lack the training, manpower and equipment needed to deal with such a large-scale crisis. And there’s a pervasive sense on Pine Ridge, a place of long-strained relations with the state and federal governments, that help has been woefully slow to arrive, and that few people beyond the reservation know or care much about its plight.

“This is a state of emergency right now,” said Henry Red Cloud, whose family’s losses in the flooding include five homes, a forklift, a truck, a van and the building where his solar energy business was based.

Mr. Red Cloud now rides a flat-bottomed boat each night to the one home on his family’s property that is not a total loss. “What we need to be doing is building sandbag walls — not a southern border wall,” he said.

Pine Ridge was far from alone in being hit with damaging quantities of snow and water this month. Huge portions of the Midwest were swallowed by rivers in the last 10 days, with devastating consequences for farms, roads and small riverfront towns. So far, at least three people are confirmed to have died, and the affected states have estimated that they have suffered more than a billion dollars in damage and economic harm.

But while conversations about recovery were already underway in the hardest-hit portions of Nebraska and Iowa, where most roads have reopened and many rivers have started to recede, Pine Ridge, with a population of about 20,000, remained in a state of hour-to-hour chaos. Some of the tribe’s scarce heavy equipment was lost in the mud. Jail inmates were enlisted to fill sandbags. New parents worried as they ran low on infant formula.

Day laborers and volunteers unload non-perishable foods from a truck during an emergency delivery by the Food Distribution Program in Oglala, S.D.

Unlike in Nebraska, where the National Guard rescued 111 people, including some by helicopter and boat, outside help for Pine Ridge was conspicuously scarce at first. South Dakota’s governor, Kristi Noem, has been seen by many Pine Ridge officials and residents as slow to respond. But Ms. Noem, who visited the reservation on Saturday, said that the tribe had only made formal requests for help in recent days, which she quickly approved. Since then, Ms. Noem said, the state had sent ATVs, a boat rescue team and a small group of National Guard soldiers to distribute drinking water.

“When we became aware is when we responded,” Ms. Noem said in an interview after her visit.

The reservation, in the southwestern part of the state, is among the most scenic places in the Great Plains states. Pine-crested buttes punctuate the skyline, open prairie stretches for miles, and creeks wind through pastures and yards. But the vast distances, scattered population and relatively untamed terrain can make it difficult to reach people in blizzards or floods.

The tribal-led relief effort on Pine Ridge has been mired in challenges. Though employees pulled marathon shifts and slept in their work vehicles, there were simply not enough people or equipment to reach everyone needing help, residents said. Julian Bear Runner, the Oglala Sioux Tribe’s newly elected president, said many had voiced frustration with the tribal government’s response.

“People are getting angry,” Mr. Bear Runner said, “and that’s understandable.” But he added, “We’re doing the best we can with what little we have.”

He said resources had been stretched so thin that he had slept on his office floor most nights since the storm, and had driven his own pickup truck to respond to calls for help because there were too few tribal workers.

Highway 28, a main route on the Pine Ridge reservation connecting Wounded Knee and Manderson, S.D., has been closed for days by flooding from nearby Fast Horse Creek.

“If we would have had state-of-the-art equipment, if we would have had adequate manpower, we could have gotten a lot done,” said Mr. Bear Runner, who said the state assistance, though late to arrive, was greatly appreciated.

Tribal officials said the federal Bureau of Indian Affairs had also provided equipment and manpower to help.

The crisis on Pine Ridge is a collision of nature, poverty and inadequate infrastructure. No sooner were Pine Ridge’s highways mostly cleared of snow than temperatures shot up, and the rush of newly melted water overflowed from creeks and rivers. The flooding — the worst in at least a generation, several residents said — turned the rugged dirt roads that many people live along into a liquefied mud soup.

Adding to the urgency, late last week about 8,000 residents lost drinking water.

“It’s gotten worse,” Mr. Bear Runner, the tribal president, said on Friday.

Pine Ridge is a place accustomed to struggle, and its people have had well-publicized battles with alcoholism and teen suicide. Half the reservation’s residents live in poverty, according to the Census Bureau, and the unemployment rate is 20 percent, compared with about 3 percent for South Dakota as a whole. Many people on Pine Ridge live in aging houses a mile or more from a highway, and some depend on wood-burning stoves to keep warm.

Garfield Steele, left, president of the reservation’s Wounded Knee District, said tribal officials were short of resources to cope with the flood. “We know people are panicked and claustrophobic,” said Babette Thin Elk, right, the district secretary. “We are doing what we can.”

“The lack of resources, the lack of water, lack of transportation and the lack of facilities — this really compounds all of the issues,” said Valentina Merdanian, a tribal council member who on Friday was fielding calls from stranded constituents and trying to organize rescue crews.

In the few quiet moments, some people expressed worry that the treacherous conditions could become a new normal. “With climate change, it’s getting worse and worse,” said Robert Pille, who had to leave his home because of the floods. “This is going to be a regular thing.”

Mr. Bear Runner said there had been no time to tally up how many buildings were destroyed, how many rescues had been made or how many people remained unreached.

“We didn’t have the proper training for the E.M.S.; we didn’t know what to do,” said Garfield Steele, the president of the reservation’s Wounded Knee District, the site of the 1890 massacre of Native Americans by United States soldiers and the 1973 siege by members of the American Indian Movement.

Governor Noem, who took office in January, has a strained relationship with her state’s Native American nations, some of which requested that their tribal flags not be displayed at the State Capitol after she introduced and lawmakers passed a set of bills this month that would restrict protests.

Despite those tensions, several people on the reservation said they would have liked to see a more robust National Guard and state government presence during the storm response. As members of the tribe volunteered to cook meals and unload food delivery trucks on Friday, and as people checked on older neighbors who lived far from the highway, some of the biggest needs remained unmet.

“We just need the technical skills,” said Mary Tobacco, who was helping lead recovery efforts, but who became stranded herself on Friday as rising water made it impossible to leave her home on a butte. (The water was moving too fast, she said, to make it out in her kayak.)

Tribal officials were still working to determine whether as many as four more deaths in the past two weeks could be attributed to the storm, including some involving patients who needed medical help and could not be reached by ambulance. The tribe’s police chief, Robert Ecoffey, said on Friday that it was not known whether those people would have survived if an ambulance had reached them.

In the meantime, some on Pine Ridge were hunkering down for what could be weeks more with little or no access to the outside world.

Bernadine Rowland, stranded since March 12, said Saturday that she and her grandchildren had remained in good spirits and had passed the days by watching Netflix and YouTube videos. But her pantry had started to get bare — only two bags of beans left, plus some oatmeal and rice — and an attempted food delivery by horseback had to be aborted Friday afternoon because a creek that had to be crossed was running too high.

Just before sunset Friday night, the horseback riders came back, this time by canoe, carrying big plastic bags full of macaroni and cheese, toilet paper, Hamburger Helper and canned pasta.

“It was a relief,” Ms. Rowland said. “We’ll have something to last us for a while.”

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