Abstract: Rocks are natural materials composed of various mineral particles within fissures and pores in different sizes, those result in complicate mechanical properties. Strength criteria for rocks in engineering design and disaster prevention are still an open question. As cohesion and friction in rock do not work simultaneously, the linear Coulomb criterion proposed in 1773 is only reliable to describe pseudo-triaxial compression strength of cylindrical specimen in a small range of confining pressure. Many nonlinear criteria are merely empirical formulas but lack of physical background. The exponential criterion proposed by the author is applicable to fit the relationship between strength and confining pressure of rocks in shear failure; therefore, the cohesion and friction are analyzed in Mohr's stress space on the fitting solutions for eleven rocks. Shear stresses in rock have an upper limit, i.e. the genuine cohesion c₀ of rock; and the internal friction has a peak of about 0.38 c₀, by which intersection of the cohesion and internal friction is. The genuine cohesion is independent to normal stress, so the nominal cohesion of rock specimen represents the shear fracture area of intact material when rock specimen reaches its strength. The equivalent friction factor of slipping fissure decreases with the normal stress, so as the climbing angle that depends on ratio of normal stress to the genuine cohesion. Relationship between the equivalent friction factor and parameters in the exponential criterion reflects the physical background of shear fracture for rock under compressive stresses.