A three-dimensional multi-fibre multi-layer micromechanical finite element model was developed for the prediction of mechanical behaviour and damage response of composite laminates. Material response and micro-scale damage mechanism of cross-ply, 0/90ns, and angle-ply, A-45ns, glass-fibre/epoxy laminates were captured using multi-scale modelling via computational micromechanics. The framework of the homogenization theory for periodic media was used for the analysis of the proposed amulti-fibre multi-layer representative volume elementa (M2RVE). Each layer in M2RVE was represented by a unit cube with multiple randomly distributed, but longitudinally aligned, fibres of equal diameter and with a volume fraction corresponding to that of each lamina (equal in the present case). Periodic boundary conditions were applied to all the faces of the M2RVE. The non-homogeneous stressastrain fields within the M2RVE were related to the average stresses and strains by using Gaussa theorem in conjunction with the HillaMandal strain energy equivalence principle. The global material response predicted by the M2RVE was found to be in good agreement with experimental results for both laminates. The model was used to study effect of matrix friction angle and cohesive strength of the fibreamatrix interface on the global material response. In addition, the M2RVE was also used to predict initiation and propagation of fibreamatrix interfacial decohesion and propagation at every point in the laminae.