Earthquake makes enormous damages when hits an area. Damages can be in human lives and structures. When a structure is connected to the earth, the connection has effects on structures and increases structure’s flexibility thereby the natural period of the structure also increases. Scattering, diffraction, reflation, and refraction change when material properties are changed. The soil structure interaction is a nonlinear phenomenon. Two essential issues are involved in the phenomenon of soil structure interaction. The first issue is kinematic interaction which deals with wave propagations. Wave propagation has effects on the structure foundation considering the geometry and stiffness properties of the structural foundation and soil. The seismic wave propagation happens by deformation in the soil medium. The foundation cannot deform by the same amount as the soil because of the foundation is considered to be very rigid in comparison to the soil deposits. So, this vision faces a mathematical difficulty which is hard to account for the mathematical models for practical vibration analysis. In this aspect, only the wave propagation in an elastic medium is involved. Therefore, the effects which starch from the wave propagation considerations is known as kinematic interaction effects. The second issue of the soil structure interaction analysis is inertial interaction. This issue deals with the deformations and stresses in supporting soil which is encouraged from the base shears and moments generated in vibrating structure. The direct and the substructure approaches are adopted in this paper to investigate the problem of soil- structure interaction. The main idea of the direct approach is including the soil medium in the mathematical model which is developed for dynamic analysis. Dynamic analysis is made by using finite element method for the domain with appropriate absorbing / transmitting boundaries. Absorbing / Transmitting boundaries prevent the seismic energy is reflected back into the problem domain. May some analysis’ results have errors if the site has deep deposits and the bottom boundary of the finite element model is placed at shallow depth instead of rock level. Deformation and stresses in the structural system are essential components of the design. The soil medium is taken as a massless medium in order to overcome the problem of owing more flexible nature of soil by the lower modes with the superstructure locating on the top of soil mass as a rigid body. This consideration inforces the modes of soil deformation to move to the higher end of the Eigen spectrum thus, providing structural modes at the lower end of the Eigen spectrum. The substructure approach is divided to three – steps solution for SSI problem. The first step is getting foundation input motion after solving the kinematic interaction problem. The second step is soil springs which are computing the frequency of dependent impedance functions. This step represents the stiffness and damping characteristics of the soil- foundation interacting system. The third step is determination the response of the real supported on frequency dependent soil springs and subjected at the base of these springs to the foundation input motion computed. The formulas which are used for soil-structure interaction analysis is taken from Pais and Kasual and modified by Gazetas. The substructure approach may be identical with direct approach if the structural foundations are completely rigid. From substructure, the approach can be concluded that the primary effect of inertial interaction in the lengthening of the natural period and increases in damping ratio of the dynamical system. Finally, this paper shows two ways of designing and modeling soil-structure interaction without determining which one is better.