This paper presents a numerical approach for estimation of effective elastic properties of carbon nanotube (CNT)-reinforced polymer composites. A square representative volume element (RVE) denoting a part of continuum is considered based on the assumption of transverse isotropy of material and the fiber/matrix regions are discretized using three-dimensional solid elements. The meshed assembly with periodic boundary conditions is employed to predict the elastic properties using finite element analysis solver. Parametric studies are conducted by considering the properties of CNT fibers both as isotropic and orthotropic, that are uniformly distributed in isotropic polymer phase. The effect of interphase properties such as its stiffness and thickness on the elastic properties is also studied. Investigated results are in good agreement with those obtained from micromechanics model.