A detailed numerical failure analysis was conducted for unidirectional glass fibre-reinforced epoxy composite laminates having an elliptical cut-out at the centre using Hashin’s damage model. The major axis, a, of the elliptical cut-out was fixed while the minor axis, b, was varied in such a way, that its upper extreme represented a situation of the plate with a circular hole, while the lower extreme of it represented the presence of a sharp crack in the structure. For angle ply cases, plies oriented along the material direction predicted an ever-increasing load replicating an elastic analysis without any damage accumulation. Such exceptionally higher stiffness and resistance to deformation were much anticipated, as the uni-axial tensile load was applied along fibre direction which shares a large portion of the load in comparison to the matrix material. While the plies oriented perpendicular to the direction of the material behaved as the weakest stack-up sequence in resisting uni-axial tensile load. Multi-angle hybrid composites predicted uneven failure behaviour. For the different combinations of multi-angle layups and minor axis, b, different trends for peak loads were observed. Interestingly, extension-shear coupling was observed for a few configurations which were marginally negligible for others. The variation of opening stress along the transverse direction predicts some very interesting observations. For the higher value of b, the opening stress decreases as we moved away from the irregularity. However, the situation of a plate with a sharp crack (b → 0) showed the effect of crack tip blunting. Near the vicinity of the sharp crack, the opening stress first dropped, then picked up, and again kept on decreasing as we move away. The drop in the stress near the vicinity of the sharp crack is attributed to the blunting of the crack tip.