In this study, an analysis of fibre reinforced, multi-layered composite plates, containing circular holes, has been carried out. First, stress concentrations around a circular hole are studied. A number of diagrams are drawn to show stress concentrations around a hole, for each layer, using different material pairs with different E-1/E-2 ratios (ratio of elasticity modulus of fibre direction to that of transverse direction). The graphs are given, for various E-1/E-2 values, for the circumferential stress values around the hole versus angular location of points, for two different fibre orientation angles. Second, the failure of the laminated composite plate is studied. For this purpose Tsai-Hill failure criterion and Hoffman failure criterion are introduced. To determine the "first-ply failure" of a laminated plate, these two failure criteria are employed. Finally, to show the effect of E-1/E-2 ratio on the failure of plates a number of tables are given for different fibre orientation angles.