Abstract In the case of composite materials such as concrete and natural rocks, fracture is resisted by internal friction, cohesion of the matrix, and adhesion at the interfaces. Although the behavior of an interface is clearly understood only when it is acted on by tensile forces, rock mechanics is primarily concerned with compressive forces. The apparent difficulty is circumvented by breaking down any given stress system into two components: an isotropic pressure and a tensile biaxial stress. The strength indicated by the latter component is precisely equal to that of the given stress system. Thus a condition of triaxial compression can be transformed into one of biaxial tension. An analysis based on this transformation indicates that the strength of composite materials in equal biaxial compression is considerably greater than in unconfined compression; this relationship becomes the keystone of a strength theory for composite materials.