An extended and verified model of single-acting hydraulic drive for cylinder valves of internal combustion (IC) piston engines has been presented. In a physical model of the valve drive system proposed, a Caterpillar electric control valve from the HEUI fuel system was used as a distributor and the function of an actuator was performed by a commercially available hydraulic cylinder. Experimental and verification tests were carried out on the physical model built on a test stand. In the model prepared, electrical, mechanical, and hydraulic parts may be discerned. The model of the valve drive system was divided into sub-models representing the control system, distributor electromagnet solenoid with variable inductance, distributor spool with the electromagnet armature, hydraulic actuator, valve with valve spring, distributor working chamber, flows through the supply gap and drain gap in the distributor, and the actuator working chamber. The models, whether originally prepared or extended during the verification tests, as well as the verification of the sub-models representing the control system and distributor electromagnet solenoid have been discussed in detail. The structure of the entire model and the relationships between input and output data of individual sub-models have been shown. The profiles of voltage and current of the control signal as well as the profiles of valve displacement and other valve motion parameters obtained from experiments have been compared with the corresponding profiles obtained from simulations. Good consistence between the experimental and simulation profiles of the valve displacement was obtained. The model thus prepared and verified became a tool for examining the properties of a single-acting hydraulic drive for the valves of internal combustion engines.