Abstract: The conventional triaxial compressive strengths of intact and damaged rocks are collected to study their properties of damage, cohesion and friction, and to reveal the influences of confining pressure on strength. The bearing capacity of a crack from friction increases with confining pressure, and the crack does not affect the strength of specimen when its bearing capacity achieves that of the materials or other cracks in neighborhood. The effect of localized damage on strength decreases with the increase of the confining pressure, and the difference of the principal stress is well fit to the exponential criterion. There is a limitation of the difference of the principal stress, or the maximum shear stress is equal to the genuine cohesion of rock materials. The genuine cohesion of marble is not influenced by the plastic deformation resulting from shear yield in the specimen, but it will decrease when the grain boundaries of the marble heated to 600℃ are seperated. The exponential criterion can describe the effect of the confining pressure on the strength of rock specimen in shear failure. However, the granite specimen compressed within the confining pressure of 20 MPa fails splitting along the axial direction, and the strength increases linearly with the confining pressure.