The inability of the Coulomb-Mohr theory of fracture to explain the main features of compression, tension, and torsion tests on brittle materials is pointed out. It is shown that the introduction of suitably chosen tension cut-offs and “friction angles” removes this deficiency and leads to a satisfactory explanation of the fracture stresses and angles of fracture for these three simple tests. The modified Coulomb-Mohr theory is a three-parameter theory, but all three parameters in principle can be obtained from only two simple tests. It is shown that in the case of cast iron there is an extremely close relationship between cohesive resistance in shear and nominal ultimate strength in single or double shear. The modified theory fits the data of Coffin, Cornet, and Grassi on biaxial fracture of cast iron very well. The three-dimensional fracture surface is described and used to explain some apparently anomalous points in the experimental data. Finally, a hypothesis is advanced which explains the appearance of concavities in the yield locus for certain classes of materials.