In this paper, the effects of the spatially varying earthquake ground motion on random hydrodynamic pressures are investigated considering dam-reservoir-foundation interaction by Lagrangian approach. For this purpose, variable-number-nodes two-dimensional fluid finite elements based on the Lagrangian approach is programmed in FORTRAN language and incorporated into a general-purpose computer program SVEM, which is used for stochastic dynamic analysis of solid systems under spatially varying earthquake ground motion. The spatial variability of ground motion is taken into account with the incoherence, wave-passage and site response effects. As the effect of the wave-passage is investigated by using wave velocities of 1000 m/s, 1500 m/s and 2000 m/s, the incoherence effect is examined by considering the Harichandran-Vanmarcke and Luco Wong coherency models. The changing of the soil conditions from firm to soft soil types are selected for considering the site-response effect where the foundation supports are constructed. The effects of transient response and the water compressibility on hydrodynamic pressures are also investigated. The ground motion is described by filtered white noise and applied to each support point of the two dimensional finite element model of the dam-reservoir-foundation system in horizontal direction. It is observed that the spatially varying earthquake ground motion affects the mean of maximum values of random hydrodynamic pressures considerably.