Several issues regarding the application of the shear and biaxial Iosipescu tests for the shear strength characterization of unidirectional composite materials are addressed in this article. First, the nonlinear effects of specimen sliding and geometric nonlinearity on the mechanical response of 0degrees standard unidirectional graphite/polyimide Iosipescu specimens with different loading conditions and loading block geometries have been investigated. Second, an attempt has been made to improve the Iosipescu shear test to eliminate normal compressive stresses in the specimen gauge section and at the same time prevent axial splitting. Finally, several Iosipescu shear and biaxial experiments have been performed to select proper specimen geometry and loading conditions for the shear strength measurements of unidirectional composites. The nonlinear effects are examined with respect to various coefficients of friction, displacements, loading angles, and fixtures (biaxial with short and modified biaxial with long loading blocks) using nonlinear finite-element techniques. It is shown that the effect of nonlinearity is small on the stresses at the center of the standard Iosipescu specimen, but significant for the stresses near the notch root up to 2 mm applied displacements. In some cases, significant differences in the stresses calculated for different coefficients of friction have been observed. All of these results are somewhat consistent for both fixtures, but with the stress components sigma x, sigma y, and sigma xy significantly lower in the standard Iosipescu specimens tested in the fixture with the long blocks. Numerical load/displacement diagrams show that specimen sliding and geometric nonlinearity have a negligible effect on reaction forces in the biaxial fixture, and a significant effect on the reaction forces in the modified biaxial fixture. Since the various combinations of the loading conditions evaluated in this study do not eliminate transverse compressive stresses in the gauge section of the standard Iosipescu specimens, a major improvement to the Iosipescu shear test has been proposed. Using an optimized specimen geometry subjected to biaxial shear/tension loading conditions, a state of almost uniform pure shear stress can be generated in 0degrees unidirectional composite Iosipescu specimens without the possibility of axial splitting along the fibers at the roots of the notches. However, it is shown in the experimental part of this study that for the optimized Iosipescu specimen, crushing at the inner loading blocks can significantly affect the shear intralaminar failure process. Only by reducing the cross-sectional area of the optimized Iosipescu specimen can the effect of crushing on the failure process be reduced without, however, highquality shear stress fields present in the gauge section at failure.