Vibration of hydraulic piston pumps has raised acute noise problems. In this work, a tandem piston pump with a swash plate is considered as a many-body combination system which has seven mass and thirty-five degrees of freedom. Motion equations expressing the entire system are used for analysis of the dynamic response of the system. Numerical analyses are performed by the Newmark-β method for discrete application of difference approximation to a matrix consisting of those equations with respect to incremental time. Satisfactory agreement between calculated and experimental responses is obtained. Then the influence of a change in the pressure pulsation phase of the tandem pump on response is clarified. By response analyses regarding pump casings by the finite element method, the influence of increased casing rigidity on response is also evaluated. It is confirmed that both the coincidence of the phase in a tandem piston pump and increased casing rigidity are effective for reducing vibration of the pump.