In this paper, a new concept for rock mass involving distributed discontinuities in the body is proposed, so called the damage mechanics theory for rock mass. The effect of distributed discontinuities is characterized with a second-order symmetric tensor (the damage tensor), which was originally proposed by S. Murakami & N. Ohno in their creep damage theory for metal. The damage tensor is built in the system of a continuum mechanics theory, and plays a role of transformation operator for the Cauchy stress. Since the damage tensor is introduced as a field variable in addition to stress and strain, one may need one more field equation which governs the propagation of damage. We propose a form of the propagation equation. The theory is applied to a few typical problems and the results are compared with ones of other numerical schemes.