Abstract：Based on the stress state at failure for coherent and frictional materials in plane strain state，it is hypothesized that the intermediate principal stress，s2，makes the Mohr circles of (s1－s2) and (s2－s3) have the same effect degree of cohesion and friction，and then the intermediate principal stress formula at failure for coherent and frictional materials in plane strain state is obtained. When coherence， ，is equal to zero，the formula becomes the one of frictional materials，and when frictional angle，j，is equal to zero，the formula becomes the one of coherent materials. At last，the relationships of strength indexes in plane strain state and those in triaxial compressive state are gained.
