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Structural elements, in many situations, are supported by other surfaces, such as soil, which may offer movement constraints in some directions. Therefore, the static and dynamic analysis of these elements considering their interaction with the soil becomes important in the design of a structural design. This paper presents the nonlinear dynamic analysis of structural systems considering such interaction through the Finite Element Method. A geometrically nonlinear beam-column element is used to model the structure, while the soil can be idealized as a continuum foundation, through the Winkler and Pasternak models. It is assumed that the foundation reacts to tension and compression stresses, so during the deformation process the structural elements are subjected to bilateral contact constraints. The analysis is based on the modeling of the structural system using the finite element method, where the Newmark integration method and Newton-Raphson iterative strategy are used in the process of solving the nonlinear dynamic equations in the time domain. Practical situations involving the interaction between soil and structure were evaluated during the study, showing the influence of contact in the natural vibration frequency and transient response of these structures.