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This paper presents a computer generated model of a hydraulic circuit that is typically seen in hybrid hydraulic vehicles (HHV's). HHV's have shown considerable potential for increasing fuel economy and decreasing emissions for mid-size and commercial trucks that exhibit urban driving habits. The aim of the present model is to aid in further optimizing the performance of the hybrid powertrain and serve as a baseline for future studies into the noise and vibration (NV) associated with the system. The model simulates the regenerative braking process of a parallel type hybrid hydraulic propulsion system. Regenerative braking captures and stores otherwise lost energy into an accumulator. This stored energy can then later be used to propel the vehicle, thus reducing the vehicle's reliance on a conventional internal combustion engine (ICE). This model will serve as a baseline for future developments and will be expanded and validated experimentally in ensuing research.