A high pressure pump including a linear actuator having a servo motor to axially rotate a hollow rotor shaft in alternating directions, the servo motor having a stator positioned co-axially around the hollow rotor shaft with an interior of the rotor shaft being co-axially coupled to a drive member to convert axial rotation into reciprocal displacement, the drive member being constrained against linear movement and supporting a shaft. At least one piston is coupled to the shaft and the piston is arranged within a cylinder to define a pumping chamber, whereby alternating rotation of the rotor shaft causes reciprocal linear displacement of the piston to pressurize fluid in the pumping chamber. A drive mechanism includes a controller coupled to a servomotor and an encoder to measure movement of the hollow rotor or output shaft and send a feedback signal proportional to the movement to the controller.