The present research considers the effect of uncertain material parameters on the stochastic dynamic response of an asphaltic lining dam-foundation system subjected to both stationary and non-stationary random excitation. The uncertain material parameters of interest are the shear modulus and mass density, which are modelled using a log-normal distribution. The Monte Carlo simulation method determines the stochastic seismic response of the dam-foundation system to spatially varying ground motion with uncertain material parameters. Consideration of the spatial variability of ground motion incorporates incoherence and wave passage effects from both stationary and non-stationary random excitations. A Heaviside modulating function is used throughout the study for the non-stationary responses. The results obtained indicate that variability of the shear modulus should be included in a stochastic dynamic analysis of an asphaltic lining dam-foundation system, but variability of the mass density can be neglected. Also, from the results, stationarity is a reasonable assumption for asphaltic lining dams in response to typical durations of strong shaking.