A numerical investigation of the seismic behaviour of asymmetrical low-rise reinforced concrete (R/C) frames is performed considering the deformability of the supporting soil. The typical rigid base assumption is adopted by most current seismic design codes for ordinary buildings, implicitly assuming that the “beneficial” influence of the Soil-Structure Interaction (SSI) effects results in a decrease of the internal forces of a structure. However, in recent research works, SSI is found to affect the structural response in not always a beneficial manner and occasionally in a detrimental one. In the current study, the non-linear time-domain seismic analyses of selected 2D and 3D symmetric and asymmetric R/C framed buildings are presented considering initially the fixed base assumption. Subsequently, these R/C building models, subjected to the same seismic excitations, are analysed considering SSI, by applying a set of orthogonal footings with tie beams which interact with the soil medium. In addition, in the 3D models, the case of a foundation mat supporting the frames is examined. Comparisons between the numerical response results obtained for the examined supporting conditions yield useful conclusions regarding the modified elastoplastic estimated behaviour of common low-rise R/C buildings due to SSI, which can be used for the improvement of the seismic design codes.