What you need to know:
- Those arriving have turned to aid groups already under strain trying to provide basic services in a country where two-thirds of the population rely on humanitarian assistance to survive.
When fighting erupted in Sudan, Rosa Yusif Elias escaped on foot with her seven children over the border to her homeland, South Sudan, where she thought they would be safe.
Instead, they have been stranded for weeks in an isolated camp that has been overwhelmed by the sudden arrival of tens of thousands of people fleeing the violence next door.
"This place is full of flies and snakes, and the food is not good," said Elias, who fled Sudan after fighting erupted between the army and a powerful paramilitary force on April 15.
She said children were coming down with diarrhoea. "In the last few days, three children have died in this camp."
The influx adds to an already dire situation in South Sudan, a troubled country that has struggled with war, famine and natural disaster since gaining independence from Sudan in 2011.
Those arriving have turned to aid groups already under strain trying to provide basic services in a country where two-thirds of the population rely on humanitarian assistance to survive.
The scene near the border is grim, with children suffering malnutrition, tensions over limited resources, and families sleeping in the open as the camp's population climbs by the day.
"We are suffering in this camp, children are dying," said Santuke Danga, who is stuck at the camp near Renk, a frontier town that has become the epicentre of this latest crisis.
"We queue up in order to get porridge for the children, at the water point people fight, (there is) no security and sometimes hyenas come."
Stretched to capacity
The UN refugee agency UNHCR said over 100,000 people have crossed from Sudan since fighting there began about two months ago -- an average of more than 1,000 per day.
Some arrive on donkeys, too weak to walk any further.
Children have been particularly affected, dehydrated and malnourished after the long journey overland through harsh country.
At a health clinic in the camp, a long queue stretched out the door.
Kony Puk waited with his one-and-a-half-year-old girl to see a doctor. She was admitted for severe acute malnutrition, a life-threatening condition.
"The child felt sick earlier, and there was no medication in Khartoum because there was fighting. That is why she is malnourished," the father of two told AFP.
"We took two weeks to arrive here, and on the road, she was only taking water and milk from her mother."
Asunta Agok, from UNHCR, said a number of people had died upon arriving, including an infant.
"The child had a very short illness, and there was no medical team on the ground to provide medical assistance," she told AFP.
The UN's World Food Programme (WFP) and other aid groups operating at the camp are stretched to capacity, and warn things could get worse as more people arrive.
"This place does not have the capacity to accommodate and facilitate these people," said Leonidace Rugemalila, WFP's head of field office in Renk.
"And with the rainy season, we could expect diseases like cholera because of the poor environment, and malnutrition cases could rise."
'Now we're stranded'
Many wish to leave the camp. But Renk, the nearest town, lies in a remote northeastern part of South Sudan without roads, where floods and armed insecurity pose very real threats to safety.
"We heard if you arrived here, we would be assisted to get home. But now we're stranded," said Christina Nyaluak Juaj, a mother of six, who used the family's single bedsheet to shield her children from the blistering sun.
Some want to travel onward as far as the capital Juba -- a distance of nearly 800 kilometres (500 miles) over swamp and wilderness, an unfathomable distance in a country the size of France with virtually no infrastructure.
With the rainy season approaching, what dirt roads do exist will become largely impassable.
"Unfortunately the poor infrastructure in South Sudan does not match the influx," said Rugemalila.
"There are no roads from Renk to other parts of the country, so it is supposed to be mainly river or air transport, which is very expensive."
Those desperate to leave face a long wait.
"We don't want to stay here... but have no means of travelling. Renk is surrounded by water, and flying is the only option, said Sadik Abdallah Almahadi, a Sudanese refugee and a father of five.
Prices for basic goods have skyrocketed in local markets due the influx.
More than 800,000 South Sudanese were living in Sudan when the conflict broke out. Many were refugees from the decades-long struggle for liberation and more recently, a devastating civil war that erupted in the south shortly after independence.
They return to a country still wracked by the armed violence and ethnic strife they fled, and scarred by four consecutive years of record flooding.
"Many communities in South Sudan are already permanently displaced by climate change, and new arrivals may come back unable to recognise or access the areas they once left," the UNHCR said Wednesday.
Stephen Tuk, 32, said he was determined to leave Sudan even if the prospect was slim of reaching his family in Bentiu, a town in northern South Sudan completely cut off by floods.
"I did not want to die in a place which is not my home," he said.