A machine for preparing liquid food products includes a pump. A cylinder is defined in the pump casing, with a piston extending in the cylinder at least in part to define a variable-volume work chamber. Between a shaft of a motor and the piston there is a transmission arrangement for causing a reciprocating movement of the piston with a predetermined stroke between advanced and retracted positions, to vary a volume of the work chamber. The pump has an intake valve and a delivery valve, for connecting the work chamber with an inlet and an outlet of the pump casing, respectively. The transmission arrangement has an actuation member driven in rotation by the shaft and operatively coupled to the piston. The actuation member defines a cam path to which the piston is coupled. The cam path is prearranged for determining the predetermined stroke of the piston between the advanced position and the retracted position.