A high pressure fuel supply pump which is driven by a cam connected to an engine is composed of a cylinder, a plunger slidably disposed in the cylinder, a tappet linked to the cam, a coil spring biasing the tappet against the cam, a cylindrical guide for the tappet, a plate member in abutment with head portion of the plunger, and a plurality of balls disposed between the plate member and the tappet to be slidable in directions perpendicular to the reciprocating motion of the plunger. Each of the balls shares the stress applied from the tappet.