In this monograph, a numerical model based on the finite element method is developed to analyze buildings with base seismic isolation, discretizing the structure-isolator system. In this way, the response of such systems is estimated with greater precision and, thus, the tasks of designing and verifying them is facilitated. The development of the model requires the resolution of the following problems: • Development of an appropriate constitutive model for elastomers that considers large elastic deformations, incompressibility, visco-elasticity and elasto-plasticity in large strains. • Incorporation of the constitutive model developed in a general model of dynamic analysis of structures using the finite element method that combines bar elements with plane elements; appropriate constitutive models for the numerical simulation of the structural materials; mixing theory; discretization by layers. • Application of damage indices that facilitate the evaluation of the global state of the structure after a seismic ground motion. • Numerical study of the behavior of structures with elastomeric isolation system subjected to earthquakes and their comparison with the corresponding fixed base structures.