Varicose veins anywhere on the body can be an ugly discovery. In rare cases, some individuals may develop small varicose veins on the penis. This is more. It tends to not share the common blue tint with a vein however. It can be felt as a hardened lump or "Vein" even when the penis is flaccid, and is even more prominent during an erection. It is fairly common and can follow a particularly vigorous sexual activity.