In order to apply the unified strength theory taking tension as positive to the rock and soil engineering customarily taking compression as positive

the experimental conditions of simple compression and simple tension tests are substituted in the expression of the unified strengththeory

and the relative parameters are determined

hence an expression of unified strength theory is derived for rock and soil materials

where compression is regarded as positive

and the difference of tension and compression strength of rock and soil materials and the effect of intermediate principal stress are taken into account. The presented unified strength theory is then introduced to establish an elasto-plastic softening constitutive model of triaxial state in strain space for a sort of diatom soft rock. A numerical simulation is carried out along with the test data of the diatom soft rock

and the result shows that the simulation of the unified elasto-plastic softening constitutive model coincides well with the test and describes the strain softening accurately.