Soil structure interaction (SSI) is the process which the response of the soil influences the motion of the structure and the motion of the structure influences the response of the soil. The interaction between the structure and soil makes the response of a structure does not depend only on the structure itself but also on the characteristics of the ground motion and the subsoil condition. In reality, the behavior of the structure under seismic load is different from what the analysis provides. Soils have different ranges of flexibilities, flexibilities play a main role in the most important design variables in seismic response of a 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. 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. RC chimney structures with raft footing are modeled with finite boundary. The RC chimneys have a width of soil medium equal to four times the width of annular raft and bedrock is assumed at 30m depth. The soil beneath the structure is modeled using both linear elastic soil models to represent the behavior of the soil. The soil structure interface is modeled with the tied surface to surface contact. The time history analysis of the soil structure model was carried out using the general FEM software SAP2000 for ground motion BHUJ. The flexibility of soil, slenderness ratio of the chimney, and thickness of annular raft are taken into consideration. All responses obtained from these models are compared with conventional method. The substructure approach may be identical with direct approach if the structural foundations are completely rigid. In conclusion, increasing the flexibility of soil decreases the natural frequency, increases in slenderness ratio of chimney decreases the tangential and radial moment of the annular raft, and decrease in radial tangential moments when a decrease in thickness of annular raft. Also, it is concluded that when the stiffness of soil is increased the deflection reduces.