The stress and strain fields in laminated composites can be described realistically with the help of a refined theory of elasticity for anisotropic materials. In contrast, the respective failure characteristics cannot be predicted satisfactorily based on the commonly used failure criteria. The main disadvantage of these generalized failure criteria, such as the quadratic failure criteria of Sakharov, Azzi/Tsai, Tsai/Wu, etc., is that they combine fundamentally different fracture mechanisms of the homogenized UD layer in one approximation by an interpolation polynomial. A completely different method for the formulation of realistic failure criteria, taking into account the heterogeneous anisotropic material structure relevant to the fracture, is based on the Mohr hypothesis for brittle materials that in fact only the stresses in the fracture plane induce failure. This physically based failure criterion not only considers the decisive difference between the fiber fracture and the interfiber fracture, but also characterizes further fracture types in the plane parallel to the fibers.