A finite-differnece scheme is presented to calculate for nonlinear conditions the hydrodynamic pressures acting on the rigid dam faces during earthquakes. The two dimensional geometry of the dam face may be non-vertical and the reservoir bottom non-horizontal. Nonlinearity of free surface flow and convective acceleration are included in the analysis. The numerical results of the onset hydrodynamic pressures acting on a constant-slope dam face and reservoir bottom due to a constant ground acceleration compare very well with those of the exact solutions. Small variations reflect the minor difference of the reservoir geometry between those two cases. Numerical results are for dam faces and compared with experimental and alternative numerical solutions. The rises of the water surface and the increases of hydrodynamic pressure on dam faces are also reported.