An investigation on fiber reinforced composite plates containing circular holes has been carried out. The stress state of a layer in a composite plate is studied for external loading. The stress concentrations around a circular hole are then studied considering stress state conditions. Glass-Epoxy and Graphite-Epoxy composites are used and stress concentrations around a hole for each material and for each fiber orientation angle are plotted. Circumferential stress values around the hole versus angular location of points, for two different fiber orientation angles and various E-1/E-2 ratios are studied along with the failure of lamina. To determine the "first--ply failure" of a laminated plate, various failure criterions are employed. Finally, to show the effect of circular holes on the failure of plates, a number of tables and figures are given.