This paper presents the advantages of using asphalt in lining dams and in asphaltic concrete core dams when comparing with clay core dams. For this purpose, the linear and nonlinear stochastic responses of a clay core dam, an asphaltic lining dam and an asphaltic concrete core dam subjected to stationary and non-stationary excitation including spatially varying ground motion (SVEGM) effects are determined by finite element method. The nonlinear response is based on equivalent linear method, which considers the nonlinear variation of soil shear moduli and damping as a function of shear strain. The results are compared with those of the responses computed using linear response for uniform ground motion and SVEGM. The spatial variability of ground motion is taken into account with incoherence and wave passage effects. Stationary as well as non-stationary stochastic response analyses are performed for three types of dam. A time dependent frequency response function is used throughout the study for non-stationary responses. It is observed from the results that it can be possible to use of asphaltic lining dams and an asphaltic concrete core dams instead of clay core dams.