The high pressure pump includes a drive shaft with at least one cam or eccentric and at least one pump element with a pump piston driven in the reciprocating direction by the cam or eccentric on the driveshaft in a reciprocating motion. A support element is arranged between the pump piston and the cam or eccentric on the driveshaft and also a roller running on the cam or eccentric is mounted to rotate therein. A support for the roller in the direction of rotation is arranged adjacent to the same in the direction of the rotational axis of the roller. The roller and/or the support include a surface with high wear resistance at least in the contact region between the roller and the support.