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Composites with various layings of unidirectional plies in the conditions of a plane stress state are considered. Using the criteria of maximum stresses and Tsai–Wu, their tensile and shear strength is investigated. The dependences of the failure stresses on the direction of loading in polar coordinates are constructed. For comparison, the results of calculations by the finite element method using the ANSYS Mechanical APDL 2020 R2 program are presented.