Abstract: The fissures in rock induce scattering strengths of specimens. However, the supporting capacity of the fissures from friction will increase up to the cohesion as the confining pressure increases. Therefore, the influence of the initial damage in rock should be less on the strengths under high confining pressures. Those strengths of granular rocks like sandstone can be fitted using the normal parabolic criterion. The parameter in the criterion is the ideal uniaxial compressive strength, and its difference with the practical test data shows the initial damage in rock. It is applicable as a key parameter in the rock damage mechanics.