What causes burst veins in fingers?

Burst veins: It's not a common description of a problem. I am not sure what burst veins is meant by. I would think injury might cause that. Possible a blood clot in the vein may cause blood pooling behind the clot and bursting some capillaries.

Several Things.: The most common cause of veins bursting and bleeding in the fingers would be trauma. Other causes could be the taking of blood thinners such as Coumadin (warfarin) but also nsaids, aspirin, fish oil, flaxseed oil, plavix, etc. Another cause could be blood problem resulting in an inability to clot. Obviously, it is impossible to make a diagnosis based on only a few facts. You should see a hematologist.