In this study, an analysis of fiber-reinforced, laminated composite plates containing circular holes has been carried out. First, the stress state of a layer in a laminated plate is studied. After obtaining the stress state for each layer due to uniaxial loading of a plate, the stress concentrations around a circular hole are studied. A number of diagrams are drawn to show the stress concentrations around a hole, for layers having different oriented fibers, using different material pairs with different E-1/E-2 ratios (ratio of elasticity modulus of fiber direction to that of transverse direction). Graphs are given for various E-1/E-2 values, for the circumferential stress values around the hole versus angular location of points, and for two different fiber orientation angles. Second, the failure of the laminated composite plate is studied. To determine the 'first-ply failure" of a laminated plate, Tsai-Hill failure criterion is employed to find minimum bearing circumferential stresses and where they occur as a function of fiber orientation angle.