This research examines the idealized and actual flow-ripple of an axial-piston swash-plate type hydrostatic pump. For the idealized case, a “perfect” pump is examined in which the leakage is considered to be zero and the fluid is considered to be incompressible. Based upon these assumptions, closed-form expressions which describe the characteristics of the idealized flow-ripple are derived. Both the ripple height and the pulse frequency of the ripple are described for a pump with an even and an odd number of pistons. Next, the actual flow-ripple of the pump is examined by considering the pump leakage and the fluid compressibility and for computing these results a numerical program is used. For both the idealized case and the actual case a comparison is made between a nine-piston, an eight-piston, and a seven-piston pump. From the idealized analysis it is quantitatively shown that the eight-piston design is less attractive than the nine or seven-piston design; however, the analysis of the actual pump flow reveals that the qualitative difference between all three designs may not be too significant. From a flow ripple point of view, the numerical results of this research show that a pump designed with an even number of pistons may be as feasible as one that is designed with an odd number of pistons. This is an unexpected conclusion. [S0022-0434(00)00202-1]