The success of mobile construction machinery owes a great deal to the proper use of hydraulic power. Hydraulic power systems are usually configured with a positive displacement hydraulic pump. Different work functions require a variety of hydraulic flow and pressure values to provide the desired operations. System branches, therefore, must include a variety of specialized flow and pressure regulating valves. The correct configuration of these valves can be accomplished by building and testing variations of a valve until desired conditions are achieved. However, since machinery build programs are expensive; the use of mathematical modeling of a fluid power component is often well worth the time required to establish the model. Use of the model to study the operation of a component will then lead to fewer hours of shop testing. This example discusses the design and mathematical model of a pressure control valve that provides priority to selected circuits on a mobile machine. The valve was used on machines with very good operational results. Agreement of operating characteristics of the valve, predicted with mathematical modeling, was found to be very consistent with the manufactured version of the valve.