An elastic plane stress finite element analysis of the stress distributions in four flat test specimens for in-plane shear response of composite materials subjected to mechanical or thermal loads is presented. The shear test specimens investigated include: slotted coupon, cross beam, Iosipescu, and rail shear. Results are presented in the form of normalized stress contour plots for all three in-plane stress components. The slotted specimen is studied for three graphite-epoxy laminates ([0], [90], [±45]_S); the cross beam is studied for two graphite-epoxy laminates ([0/90]_S, [±45]_S); the Iosipescu and rail shear specimens are studied with several materials (steel, graphite-epoxy, and graphite-polyimide) and several laminates ([0], [90], [0/90]_S, [±45]_S, [0/90/±45]_S) with rigid and elastic fixtures loaded mechanically or thermally. Geometric alterations are also investigated. The study shows that the cross beam, Iosipescu, and rail shear specimens have stress distributions which are more than adequate for determining linear shear behavior of composite materials. Laminate properties, core effects, and fixture configurations are among the factors which were found to influence the stress distributions. / Master of Science