This work represents a comparative study of available analytical micromechanical models used to evaluate the elastic properties of unidirectional (UD) composite material with long fibers (where the ratio Length/Diameter of the fibers is considered to be infinite). The objective of this work is to find the appropriate model, to be used with different volume fractions of fibers, to determine the micromechanical elastic properties. This study is carried out due to the importance of using the suitable micromechanical model, when modeling bi-dimensional and tridimensional composite materials. The models are divided into two different categories: rheological, and inclusion models. The UD composite material represents a transversely isotropic material composed of two phases: the reinforcement phase and the matrix phase. Isotropic fibers (e.g. glass fibers) or anisotropic fibers (e.g. carbon fibers) represent the reinforcement phase while an isotropic material (e.g. epoxy) represents the matrix phase. In this study only longitudinal and transversal Young’s moduli are discussed. Analytical and Finite element modeling is made for a carbon fiber/epoxy UD composite. The obtained analytical results are compared to those obtained numerically and to the available experimental data. The analytical results are evaluated for different values of fiber volume fraction Vf ranging from 0 to 1.