The article presents a micromechanical study to investigate the effective response of carbon fibre reinforced plastics (CFRP). A Representative Volume Element (RVE) approach has been used to model the material microstructure. Monte Carlo method-based Random Sequential adsorption algorithm (RSA) has been used to imitate the random microstructure of the CFRPs. A thorough comparison between the random and uniform microstructures has been shown to account the effect of randomness in the material. Fibres have been modelled as elastic and transversely isotropic, whereas the inelastic nature of the matrix has been modelled using classical J2 plasticity criterion. A three-dimensional boundary value problem with six (three normal and three shear) standard cases have been solved using finite element methodology. The computation has been performed using ABAQUS/CAE software. A UMAT material subroutine in FORTRAN has been used to include the different material models for fibre and matrix. Parametric studies have been performed to demonstrate the effect of fibre volume fraction and RVE size on the effective response of the materials.