The ulnar artery is located in the elbow, and it is one of the branches of the brachial artery. The ulnar artery leads down the ulnar side of the forearm to the wrist. Some of the branches supply blood to the area around the elbow-joint, while others supply the flexor and extensor muscles in the lower arm. At the wrist, branches of the ulnar and radial arteries join to form a network of vessels, which supply the structures in the wrist, hand and fingers. The corresponding ulnar vein will parallel the brachial artery on its way back to the heart.