The failure mechanisms, as well as the indentation and penetration resistance, of carbon fibre reinforced plastic (CFRP) cross-ply laminates were investigated under quasi-static and ballistic loading. In this thesis, the two most prominent failure modes were indirect tension and shear plugging. To characterise the indirect tension mechanism, CFRP cross-ply coupons with various matrix shear strengths were subjected to uniaxial out-of-plane compression between lubricated platens, while CFRP cross-ply beams were subjected to quasi-static indentation between a flat bottom indentor and a lubricated back support. The out-of-plane compressive strength was accurately predicted by finite element simulations and analytical models. To characterise the shear plugging mechanism, quasi-static cropping tests were performed on CFRP cross-ply beams. A beam configuration was selected to allow for ease of identifying the failure mechanisms. The investigation was extended to consider the effect of matrix shear strength on the ballistic performance of simply supported CFRP cross-ply beams impacted by a flat projectile. Laminates with high matrix shear strength failed by shear plugging, and the penetration velocity increased with decreasing matrix shear strength. As the matrix shear strength decreased further, the failure mode switched to indirect tension and subsequently the penetration velocity remained elevated, independent of the matrix shear strength. Having established that shear plugging is associated with low impact resistance, a new type of bilayer CFRP composite (comprising one low and one high matrix shear strength layer) was developed with the intent of suppressing this shear plugging mode. The ballistic penetration resistance of the bilayer beams was compared to that of the above monolithic CFRP beams using the same ballistic set-up. It was observed that the shear plugging mode in the high strength layer was suppressed when the layer was placed at the distal face; failure switched to a back face tensile mode, and the impact resistance was improved. The investigation was extended to a more realistic impact environment: CFRP cross-ply laminates in a plate configuration were perforated by a steel ball. Specimens were tested under quasi-static and ballistic loading with either a back-supported condition (simulating a thick laminate) or an edge-clamped condition. The CFRP plates failed by indirect tension when back-supported but failed by shear plugging when edge-clamped. It was found that the addition of a protective aluminium alloy layer did not alter the failure mechanism of the CFRP, but did produce a load spreading effect that increased the penetration resistance.