This paper describes a study of the cylinder pressure and flow in an oil hydraulic axial piston pump. A comparison is made between a theoretical model based on the effects of fluid compliance within the cylinder, and an improved model which accounts for the influence of oil momentum in the port plate region. The improved model is validated by comparison with experimental test results and is used to analyze the influence of port plate and relief groove design on cylinder pressure and pump flow ripple. A steeply sloping triangular cross-section groove was found to be the most satisfactory design.