A compliant bone drill provides advantages over conventional straight drills, because it allows surgical access via a minimally invasive approach. Hydropower allows the transfer of pressurized water with a compliant hose. The goal is to select the hydraulic actuator for this compliant bone drill by reviewing existing actuator principles. The selection was performed with a theoretical analysis. Design requirements were derived from a challenging minimally invasive bone drill procedure, and were set: a speed of 750 rpm, a torque of 0.015 Nm and a maximum dimensional volume of 5 mm × 5 mm × 10 mm to drill Ø 1.5 mm holes in human bone. A literature search was performed. For each actuator, the fluid flow and the required pressure difference were described as a function of the actuator dimensions and the rotational speed. Selection of the actuator was performed by it meeting the set output power, the torque, realistic input dimensions, and requiring the lowest pressure and number of parts. Existing literature provided six hydraulic actuators: external gear motor, gear ring motor, axial turbine, radial turbine, Pelton wheel, and Ossberger turbine. The latter four are hydrodynamic turbines, which could not meet the rotational speed. The external gear motor was selected for its lowest required pressure difference (11.5×105 Pa) and design simplicity. This theoretical design approach can be used for other applications.