A vascular incision apparatus is composed in part of a needle for puncturing a blood vessel and a cutter for making an incision in the blood vessel. The apparatus easily, rapidly and reliably creates a vascular incision of the desired length by employing an incision length controlling means to control the length of penetration by the needle into the blood vessel, or by controlling the distance between the respective needle points on first and second needles which face each other across a given distance, one of which needles is movable relative to the other.