In this study, the mechanical properties of unidirectional fiber composites were determined by using the representative volume element method. The aim of this study was to determine the equivalent elastic constants for the "fiber composite polymer (PPE/PP) thermoplastic material" used in a wide variety of engineering applications. At the first step, the micromechanical model was applied to the polypropylene (PP) fiber-matrix composite, and then the microstructure form of the material was analyzed by finite element method considering "rule of mixture". The symmetry boundary conditions have been applied by using the representative volume elements in 3D finite element models. The SOLID187 mesh element of ANSYS was used for the presentation of the microstructure form of the fiber-matrix composite. The elastic constants obtained in this study were respectively as follows: the longitudinal elastic modulus and the Poisson ratio E-1, nu(12), the transverse elastic modulus and the Poisson ratio E-2, nu(23). For verification, the numerical results were also compared with the literature.