The Soil–Structure Interaction (SSI) effect has been widely evidenced during several earthquakes around the world. In the Venezuelan context, the seismic event in Caracas in 1967 showed the significant consequences of designing buildings without considering the SSI effect. Nevertheless, limited research on the seismic performance of concrete moment frames (commonly used as structural systems in office and residential buildings in Venezuela and Latin America) considering the SSI effects has been developed, although there have been continuous updates to the Venezuelan Seismic Code. In this research, the influence of the SSI on the seismic performance of RC moment frame buildings designed according to the New Venezuelan Seismic Code was studied. An extensive numerical study of 3D buildings using concrete moment frames supported by mat foundations on sandy and clayey soils was performed. The response spectrum method, non-linear static analysis, and non-linear dynamic analysis were used to assess the seismic response of the archetypes studied. The results show that SSI effects can have a significant impact on the seismic response of RC moment frame buildings, increasing the interstory drift ratio and decreasing the shear forces. As is shown in fragility curves, the probability of collapse increases for cases with flexible bases in comparison to the cases of models with fixed bases. Additionally, in the 24-story archetype, the fixed-base model reached a maximum probability of collapse. Finally, a new proposal for the reduction of the strength-reduction factor (R) must be incorporated into the Venezuelan Seismic Code to improve the safety of the structures. Limitations in the use of RC moment frames must be incorporated for high-rise buildings since, as the present work demonstrates, for high-period structures, the normative provisions are not reached.