This paper, presents the static analysis of composite beams with transverse shear effects using polynomials based dimensional reduction method. In dimensional reduction method, a three dimensional elasticity problem is split into a two dimensional cross section analysis and a one dimensional beam analysis. FEM is commonly used to analyze beam cross section in the literature. In this study, polynomial functions and Rayleigh-Ritz method are used to present an analytical procedure for two dimensional cross section analysis. Variational Asymptotic Method (VAM) is employed considering shear stiffnesses of composite beam cross section. VAM, asymptotically generates fully coupled cross section stiffness matrix. VAM benefits small parameters, related to characteristic length of cross section, to find stationary values of beam energy functional. By minimizing the energy functional with respect to warpings, in and out of plane warping functions are acquired. In this article, isotropic beams with different cross section geometries and symmetric as well as anti-symmetric composite box beams are investigated. Presented results show appropriate correlation of the present study with theoretical and experimental results, as well as 3D Finite Element analysis. Using dimensional reduction method reduces the computing time and empowers researchers to design and optimize composite beam-like structures.