A fuel injection pump for internal combustion engines having a pump piston reciprocating in a cylinder to inject fuel from a working chamber into the engine cylinders and in which the termination of each injection is determined by an engine r.p.m. device which opens, or partially opens, a relief bore connected between the working chamber and a pump suction chamber. The outlets of the relief bore located on the surface of the pump piston are so formed so as to cooperate with the r.p.m. responsive device to match the injection requirements of the internal combustion engine. Several embodiments of the formed outlets are disclosed.