Three-dimensional computation on the interaction of the internal flow and the oscillating surface of a piezoelectic pump has been carried out. A general flow solver based upon the multi-domain method and the semi-Lagrangian time integration method was employed to solve the viscous flow inside the pump. The oscillating surface was modeled to account for the effects of the mass, the elasticity, the dumping factor, the pressure difference and the piezoelectric force. Computations were conducted for piezoelectric forces of different frequency. The details of the interaction of the internal flow and the surface were clarified. The frequency, which results in the maximum deformation of the surface as well as the flow rate, was determined.