In this paper, a set of MR valves is implemented within a Wheatstone bridge hydraulic power circuit to drive a hydraulic actuator using a gear pump. A compact hydraulic power actuation system is developed that is comprised of a Wheatstone bridge network of magnetorheological (MR) valves with a conventional hydraulic cylinder. There are many advantages of using MR valves in hydraulic actuation systems, including: valves have no moving parts, eliminating the complexity and durability issues in conventional mechanical valves. In such a system MR fluid is used as the hydraulic fluid. A constant volume pump is used to pressurize the MR fluid which eliminates the effect of fluid compliance to a large degree. If a change in direction is required, the flow through each of the valves in the Wheatstone bridge can be controlled smoothly via changing the applied magnetic field. A magnetic field analysis is conducted to design a high-efficiency compact MR valve. The behavior and performance of the MR valve is expressed in terms of non-dimensional parameters. The performance of the hydraulic actuator system with Wheatstone bridge network of MR valves is derived using three different constitutive models of the MR fluid: an idealized model (infinite yield stress), a Bingham-plastic model, and a biviscous model. The analytical system efficiency in each case is compared and departures from ideal behavior, that is, a valve with infinite blocking pressure, are recognized.