The present article investigates the analytical and computational derivation of the moduli of continuous fiber-reinforced composites. Theoretical expressions for the longitudinal and transverse elastic moduli and also for the longitudinal and transverse Poisson ratios, which were derived taking into account the concept of boundary interphase between fibers and matrix, were obtained as a function of the fiber volume fraction. The micro-scale model considers that the composite material consists of three phases: the fiber, the matrix, and the interphase. The latter is the part of the polymer matrix lying at a close vicinity to the fiber surface. In this investigation, it was assumed that the interphase is inhomogeneous in nature with varying mechanical properties. Different laws of variation of its elastic modulus and Poisson ratio were taken into account in order to define the overall modulus of the composite. Thermal analysis method had been used for the estimation of the thickness of the interphase. An investigation about the influence of an interphase region on the elastic constants given by the rules of the mixtures is also carried out. Finite element analysis was performed in order to obtain the elastic constants and to compare them with the respective theoretical values derived from the interphase model and with those from other models and also with experimental results.