The accurate analysis of the seismic response of isolated structures requires incorporation of the flexibility of supporting soil.However,it is often customary to idealize the soil as rigid during the analysis of such structures.In this paper,seismic response time history analyses of base-isolated buildings modelled as linear single degree-of-freedom(SDOF) and multi degree-of-freedom(MDOF) systems with linear and nonlinear base models considering and ignoring the flexibility of supporting soil are conducted.The flexibility of supporting soil is modelled through a lumped parameter model consisting of swaying and rocking spring-dashpots.In the analysis,a large number of parametric studies for different earthquake excitations with three different peak ground acceleration(PGA) levels,different natural periods of the building models,and different shear wave velocities in the soil are considered.For the isolation system,laminated rubber bearings(LRBs) as well as high damping rubber bearings(HDRBs) are used.Responses of the isolated buildings with and without SSI are compared under different ground motions leading to the following conclusions:(1) soil flexibility may considerably influence the stiff superstructure response and may only slightly influence the response of the flexible structures;(2) the use of HDRBs for the isolation system induces higher structural peak responses with SSI compared to the system with LRBs;(3) although the peak response is affected by the incorporation of soil flexibility,it appears insensitive to the variation of shear wave velocity in the soil;(4) the response amplifications of the SDOF system become closer to unit with the increase in the natural period of the building,indicating an inverse relationship between SSI effects and natural periods for all the considered ground motions,base isolations and shear wave velocities;(5) the incorporation of SSI increases the number of significant cycles of large amplitude accelerations for all the stories,especially for earthquakes with low and moderate PGA levels;and(6) buildings with a linear LRB base-isolation system exhibit larger differences in displacement and acceleration amplifications,especially at the level of the lower stories. The accurate analysis of the seismic response of isolated structures requires incorporation of the flexibility of supporting soil. However, it is often customary to idealize the soil as rigid during the analysis of such structures.In this paper, seismic response time history analyzes of base- isolated buildings modelled as linear single degree-of-freedom (SDOF) and multi degree-of-freedom (MDOF) systems with linear and nonlinear base models considering and ignoring the flexibility of supporting soil are the flexibility of supporting soil is modelled through a lumped parameter model consisting of swaying and rocking spring-dashpots.In the analysis, a large number of parametric studies for different earthquake excitations with three different peak ground acceleration (PGA) levels, different natural periods of the building models, and different shear waves velocities in the soil are considered. For the isolation system, laminated rubber bearings (LRBs) as well as high damping rubber bearings ( HDRBs) are used. Responses of the isolated buildings with and without SSI are compared under different ground motions leading to the folds: (1) soil flexibility may seem influence slightly over the stiff superstructure response and may only slightly influence the response of the flexible structures; (2) the use of HDRBs for the isolation system induces higher structural peak responses with SSI compared to the variation of shear waves (3) although the peak response is affected by the incorporation of soil flexibility, it appears insensitive to the variation of shear wave velocity of the soil; (4) the response amplifications of the SDOF system become closer to unit with the increase in the natural period of the building, indicating an inverse relationship between SSI effects and natural periods for all the considered ground motions, base isolations and shear wave velocities; (5) the incorporation of SSI increases the number of significant cycles of large amplitude accelerations for all the stories, especially for earthquakes with low and moderate PGA levels; and (6) buildings with a linear LRB base-isolation system exhibit larger differences in displacement and acceleration amplifications, especially at the level of the lower stories.