Most of laminated composites used in modern structures exhibit nonlinearity even under elastic conditions. Probably, the most evident case that reveals this effect is the plane shear experiment, where the stress strain diagram is apparently nonlinear directly from low values of load. This experiment demonstrates the decrease in shear modulus during increase of shear stress and strain. The aim of the research is the analysis of shear nonlinear response of the composite material with stress concentrator, and its influence on stress distribution and damage evaluation during specimen loading. An example problem of an open hole composite plate under compression loading is studied. The comparison of experimental and numerical results is performed with reasonable proximity. It was shown that in spite of equal limit loads of the nonlinear elastic model and linear one, the stress and damage distributions are significantly different.