Multiscale micro-mechanics theory is extensively used for the prediction of the material response and damage analysis of unidirectional lamina using a representative volume element (RVE). This paper presents a RVE-based approach to characterize the material response of a multi-fibre cross-ply laminate considering the effect of matrix damage and fibre-matrix interfacial strength. The framework of the homogenization theory for periodic media has been used for the analysis of a 'multi-fibre multi-layer representative volume element' (M2RVE) representing cross-ply laminate. The non-homogeneous stress-strain fields within the M2RVE are related to the average stresses and strains by using Gauss theorem and the Hill-Mandal strain energy equivalence principle. The interfacial bonding strength affects the in-plane shear stress-strain response significantly. The material response predicted by M2RVE is in good agreement with the experimental results available in the literature. The maximum difference between the shear stress predicted using M2RVE and the experimental results is ∼15% for the bonding strength of 30MPa at the strain value of 1.1%.