A finite difference version of the Dynamic Relaxation (DR) method is used to generate elastic solutions of the small and the large deflection Mindlin plate equations for unsymmetrically laminated cross-ply strips subjected to uniform lateral pressure. The Maximum Stress (Independent) and Tsai-Hill failure criteria are combined with these solutions to produce initial failure analyses. It is shown that coupling between bending and stretching due to the B11 stiffness term can cause a considerable increase or decrease in the flexural stiffness of simply supported in-plane fixed strips relative to the equivalent orthotropic strips but not necessarily in the corresponding failure pressures. It is also found that the predictions of the two failure criteria are in close agreement.