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.The soil structure interaction is an eternal issue that may affect the actual behavior and design of the structures. For many years the civil engineers are dealing with this issue as an important issue and should be investigated. In this study, the conventional finite element method is adopted. Also, the effects of some important analytical modeling parameters on the dynamic response of structures under horizontal and vertical ground motions are taken into considerations. Structural type, aspect ratio, the soil mass, dimension of soil model, and boundary conditions are important effects on design and analysis of soil structure interaction, therefore, this study focuses on these effects. The structural system in this study consist of 5,10,15 stories moment resisting frame and concentrically braced frame. Aspect ratios of (height: base) 1:2, 1:1, 2:1 are adopted with story height of 3 meters. Under all structures, a continuous reinforced concrete foundation is assumed. The soil- structure system also has a soil media with a constant depth of 80 meters. Two general methods of soil structure analysis are used in research. The first one is the sub-structure method which is defined by using an artificial border immediately under the base of the structural foundation and the concept of dynamic impedance of the unbounded soil media. The second one is a direct method which is directly part of the unbounded soil media. Using direct method seems more appropriate with finite element software. Iranian seismic code (Standard 2800, BHRC, 2005) is used assuming a fixed base, soil type III and maximum ground acceleration of 0.35g and designed according to part 10 of national building regulations (INRB, 2008). Also, Soil has shear wave velocity of 300 m/s, deformation modulus of E = 466 N/mm2, poison ratio v = 0.35, and density of 18 KN/m3. Sap2000 program is used for finite element modeling of the soil-structure problem. Two dimensions plane strain elastic elements are used for modeling and two alternatives of soil modeling are selected. The first alternative (mass) which includes the mass of soil. The second alternative (massless) does not include the mass of soil. Nonlinear GAP connector elements are used between the reinforced concrete foundation of the structure and the soil in order to complete the soil structure construction of the soil-structure model. GAP connectors consist of an elastic spring and an incorporated opening so that no tensile forces are transmitted between the structure and the soil. The behavior of GAP element is linear elastic under compressive forces. The GAP elements are put in every-one meter along the length of the structural foundation with high spring stiffness value (104 KN/m). The damping is assumed as 4% of the critical damping using Rayleigh damping definition. The boundary conditions for the analytical model are represented for horizontal and vertical soil boundaries. For horizontal soil boundaries, a fixed boundary is assumed at the base of the soil model. But, for vertical soil boundaries, three alternatives are assumed. First free boundary, within these boundaries the displacement at the side boundaries are free from any constraints and take place vertically. Second tied boundaries, in these boundaries the corresponding nodes on two vertical boundaries at two sides of the soil model are tied to each other thus their horizontal and vertical displacement are the same all times during the analysis. Third transmitting boundaries, these boundaries are presented by viscous dampers at the boundaries. These dampers can absorb body waves propagation to the boundary. Three ground motions with horizontal and vertical components are selected for dynamic analysis. Selection depends on soil type and seismic hazard scenario considered in the design of the structures. The selected ground motions are Cape Mendocino, Duzce Turkey, and Loma Prieta. These ground motions are applied to the fixed base of the soil model. All responses are considered in terms of maximum base shear and interstory drifts. Further, responses are compared to each other in different models as well as the models without soil-structure interaction. It has been noticed that the soil model does not have an effect on the propagation of waves, thereby, for massless soil models the free ground motions are directly applied. Also, for the free field response, it is noticed that the model with tied boundary conditions performs well in simulating the free field motion both at the near and far point of soil system and under both horizontal and vertical component of the earthquake. Soil domain size does not have any effects on the base shear value for different structures. When the structure is present on the soil layer the ground motion characteristics near to the structure and the extent of the modifications change due to the structure height (period), and type of the structure and earthquake. The type of boundary modeling directly affects the seismic response of different structural models. Moreover, it is noticed that the increase of the height of the structure is also increasing the seismic response of different structures models which have different boundary types. But for the small structures, the response values are closed to each other. The dynamic SSI may affect the seismic responses depending on the characteristics of the soil and structure. Also, taking SSI into consideration increases the drift values especially in tall structures. In addition, tied boundary modeling has clear performance better than free and transmitted boundaries. Finally, the researchers suggested that this study needs more accurate modeling by using available more advanced analytical tools.