One of the problems of a hydraulic hybrid vehicle (HHV) reported from testing by EPA is that the noise levels emitted by the hydraulic system are not acceptable. The pump is the main source of noise in HHV systems. However, the lack of space, the high pressure, and the dynamics of components within the pump have prevented either direct observation or measurement of potential noise causing mechanisms within the pump structure. As a result, there are several theories as to the source of the noise from the pump units but little concrete information to further isolate and reduce the noise generation. In this paper, a kinematic and a geometric model of a bent-axis pump have been created as part of a complete dynamic model. The other elements of the complete dynamic model that are not discussed in this paper include finding the variation of piston pressure, flow rate, and dynamic forces acting on the pump components as a function of angular rotations of both the main shaft and the yoke in the time and frequency domains. These elements address the harmonics of the forces acting on the case of the pump and will be presented in a future paper. The model was constructed using MATHEMATICA ™ software and verified against very well known conditions of the motion of the main shaft and the yoke. It was found that the model predicted the variations of the angular velocities and accelerations of the entire pump’s parts starting from the main shaft to the yoke.