The Boundary Element Method (BEM) is a numerical tool to describe the stationary dynamic behavior of foundations interacting with soil profiles. For transient analysis, the BEM is computationally expensive and limited to a relatively small number of time steps. The approach proposed in this work is based on a stationary 3D BEM analysis. Frequency domain analysis using DSSI typically consists of two steps. First, the synthesis of dynamic impedances of a rigid and massless foundation interacting with the soil. The following step involves including the foundation’s inertia characteristics into the BEM model, which leads to the frequency response of the system. In the present work shows that if a small amount of mass (or inertia) is added to the originally massless foundation it will result in a Frequency Response Function (FRFs) of the system, in which resonances are present. From these FRFs it is possible to extract a set of modal parameters which permits the synthesis of a set of ordinary differential equations in time domain reproducing the transient behavior of the soil-foundation system. In other words, the stationary response of the soil-foundation system is transformed into an equivalent set time-domain ordinary differential equations of the type M-C-K (mass-damping-stiffness). This set of MCK time domain equations can be numerically integrated leading to accurate transient response with arbitrarily small-time steps and arbitrarily long periods of time [1]. Moreover, these equations can be iteratively combined with any other linear or nonlinear structures supported by the foundation. The present work investigates the amount of inertia that must be added to the massless foundation to obtain a discrete system of equation that accurately reproduces the transient dynamics of the soil-foundation system. Distinct classical soil models are considered. This approach is evaluated for both its precision and computational expense, in relation to other available methods.