In this study, an analysis of fiber reinforced, symmetrically 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 the 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 E1/E2 ratios (ratio of elasticity modulus of fiber direction to that of transverse direction). Graphs are given for various E1/E2 values for the circumferential stress values around the hole versus angular location of points 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 the fiber orientation angle.