"The two-dimensional theory of two simple generalizations of the Coulomb-Navier criterion for shear failure is developed. The first of these refers to a material with a single plane of weakness which has a different shear strength and coefficient of internal friction from the remainder of the material. In this case it is shown that failure may take place, according to circumstances, either in the plane of weakness or in planes cutting across it. The second criterion refers to a layered material whose shear strength varies continuously from a maximum in one direction to a minimum in the perpendicular direction. In this case it appears that, instead of the two directions of failure possible for an isotropic material, there is only one possible plane of failure which lies between the plane of minimum shear strength and the nearest to it of the two Coulomb-Navier planes. Numerical results are given for the case of uniaxial compression and experimental results are shown to be in reasonable agreement with them."