In order to understand the strength failure under complex stresses

and apply the strength theory to more materials

such as rocks and concrete

by the twin strength theory

the three-parameter twin strength criterion based on the hydrostatic pressure and the normal stress on the surface of main shear stress has been proposed

and the mathematical formula has been deduced. Then the comparative analyses between the theories under different stresses with the existing experimental data have been carried out. The results show that the ratios and under different ultimate stresses vary with different strength criteria respectively and the strength under condition of is less than that the strength under condition of . In the biaxial compressive stress

the biaxial compressive strength is larger than the uniaxial one . In triaxial compression stress

given fixed and smaller

increases gradually with the increase of

and given relatively larger

decreases gradually with the increase of . The theoretical predictions can reflect some experimental data of the granite

red sandstone

soft sandstone

concrete and other materials.