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Arational approach is introduced for numerical modeling of unbounded soil foundations based on coupled dynamic periodic infinite and conventional finite elements (IFE-FE). The model can be applied for analysis of various dynamic problems in geomechanics, especially in Soil Structure Interaction (SSI), where determination of stiffness properties and response of unbounded soil domains are of prime importance. In numerical SSI analysis, there exists important problems a) the discretization of natural soil foundation, especially defining the boundaries to prevent reflecting body waves and avoiding spurious results, b) the definition of the matrices related to the soils impedance functions which are essentially dependant on the excitation frequency, c) the evaluation of free field motion of the natural foundation, especially those of irregular geometry and material diversity. An efficient way and integrated solution to these important problems is found to be the use of periodic infinite elements. The wave equation of motion is derived numerically for discretization of the soil domain. Shape functions and mapping coordinates for dynamic periodic infinite elements are presented in this paper. The accuracy of the IFE is examined for the evaluation of free field motion of a visco-elastic soil foundation. Derivation of impedance function is shown and leads to the determination of dynamic stiffness characteristics of the unbounded soil medium including spring and dashpot coefficients. Application of the approach introduced here is shown by analysis of SSI for a semi-tall building subjected to earthquake loading. Other advantages of the approach are the substantial reduction in degrees of freedom involved in numerical SSI analysis, the computational time and costs without sacrificing the accuracy of the results.