In recent years composite materials find wide application in various fields of engineering, because they have a number of advantages over other structural materials. A variety of composites' physical and mechanical properties (especially anisotropy) requires an improvement of existing calculation methods and creation of new ones for structural elements made of these materials. This is an important task which will contribute to their wider use. In this paper some famous criteria of anisotropic materials are examined, and their advantages and disadvan-tages are discussed. The authors of the paper suggest new variants of strength criteria for anisotropic materials. These new criteria are based on new mechanical characteristics which are more convenient for experimental obtaining. Also new criteria use separate form of writing for each quadrant of the stress plain. © Published under licence by IOP Publishing Ltd.