In this paper an orthotropic material is considered in the form of unidirectional composites reinforced by parallel lay fibers and layered composites which are stacking up of unidirectional plies. The structural-phenomenological model is used based on both the criteria of maximum stresses and the Tsai-Wu criterion to assess fracture of composite material. Dependences of the strength characteristics of orthotropic materials on the loading direction are built for a plane stress state. The authors show that in some cases, the criteria for maximum stresses and Tsai-Wu lead to significantly different results. Moreover, for quasi-isotropic structures, in contrast to elastic constants the ultimate stresses depend on the loading direction. This dependence becomes more noticeable under shear.