The article presents a theoretical analysis of a roller pump design and a summary of the experiments. The pump is to provide high pressure for transmission, accessory drive, and other applications. A theoretical model was built to simulate the motion of the rollers and optimize the design. An experiment was conducted to prove the simulation.The mathematical model was built within constraints of rigid body mechanics. Comprehensive kinematic and force analysis was done through differential equations of motion. Obtained quantitative relationships include, on one hand, pump geometry, speed of rotation, and discharge/suction oil pressure, and, on the other hand, torque, dynamic interaction of relatively moving parts, and kinematic parameters of the roller. The model includes dissipate forces to account for hydraulic effects. Modeling these forces is beyond mechanics of solid body and is not considered at this initial stage of research. The simulation used matrix algebra, recursive methods of solving non-linear system of equations, ordinary differential equations. Calculations were done by means of MathCad7 Professional software in a MathConnex frame. Tests were conducted on a hydraulic pump test stand with capabilities to set and measure speed, pressure, torque, flow, and temperature.The research showed that a mathematical model built on fundamental scientific basis and strengthened with modern computer tools is valid for explaining available experimental facts; therefore, it may be used for optimizing geometry the model is flexible: new components, such as those representing hydrodynamic effects, may be easily added for better approximation both calculations and experiments revealed some drawbacks of the design; nevertheless, further development is feasible.