The problem of random vibration analysis of gravity dam reservoir system subjected to spatially varying multi-component ground motion is considered. The work is done in two parts. First part deals with seismic wave propagation modelling in a three-dimensional elastic medium caused due to a seismic disturbance at a specified location in the interior. The disturbance is modelled as an effective point source of slip characterised by an impulsive double couple varying in time as a spatially localised infinite duration ramp function on the fault plane. A frequency domain wave propagation model that incorporates damping behaviour via a complex modulus representation is employed. The time domain representation is obtained further using Fourier integral. An ensemble of ground motions is simulated by treating various source parameters and properties of the intervening medium as uncertain. In the second part of work, governing equations for the dam reservoir system are formulated in which the ground motions derived in the previous step appear as boundary conditions. This set of equations is subsequently analysed using the finite element method to characterise the dynamic response of the system considering fluid structure interaction. This, in turn, forms the basis for investigating reliability of the dam structure with respect to a set of limit states. Furthermore, the analysis also leads to the determination of seismic fragility curves. While the problem of seismic response of dam reservoir system has been widely studied in the existing literature, present study permits us to examine the role played by spatial variability of support motion and their non-stationary and non-Gaussian features.