Humanitarian workers say that each day, up to 700 people cross the border from South Kordofan into Yida in neighbouring South Sudan.
The refugees are fleeing the ongoing violence in their home state.
Aid workers say they are scaling up their operation to cope with the influx.
But they are concerned about the dangers these refugees still face, as they remain close to the conflict zone.
Al Jazeera's Haru Mutasa reports from Yida in South Sudan.