This paper presents a comprehensive model of a hydraulic power steering system for predicting the transient responses under various steering inputs. The first principles of multi-body system dynamics and fluid mechanics are applied to model key nonlinear components and in particular, the rotary spool valve, piped fluid lines, the frictional coupling between multiple contacting surfaces with use of the empirical data. The system model, which integrates together all of lump masses, fluid line elements and hydraulic components, is formulated using the state space representation approach. It contains time-variant coefficient matrices resulting from the nonlinearities in the fluids systems. A numerical simulation scheme is developed to obtain the system transient responses and the results are compared with those measured from the tests. Large transient vibration (or judder) of multi-body subsystem, or pressure ripple in the hydraulic subsystem, are observed from both of simulation and tests under certain operating conditions. In general, the simulation results agree with those obtained from the tests under the same steering inputs and operating conditions. The presented model can predict the pressure boosting characteristics of the rotary spool valve with a good accuracy, which could otherwise only be done through testing on prototypes.