A detailed study on micromechanical constitutive modelling of unidirectional fiber reinforced and plain woven textile composites (PWTC) is performed. The primary objective is to compute the equivalent homogenized effective properties of PWTC through its mesoscale model. A novel parallel-series model is proposed, to compute the engineering constants in transverse plane of unidirectional composite, and validated against Chamis approaches, Mori–Tanaka and finite element method results for glass/epoxy composite. Computational homogenization of representative volume element (RVE) of transverse direction unidirectional composite is performed satisfying the periodicity of RVE. The RVE of PWTC is then approximated as cross-ply laminate consisting warp and fill plies, whose averaged properties are computed considering fiber undulations by micromechanics-based models. The bounds of the effective material properties of PWTC are determined employing Voigt and Reuss approximation. The effective engineering constants of glass/epoxy PWTC computed are compared with in-house experiments and found to be closely matching with Voigt model. © 2017 Elsevier Ltd