Abstract: According to the shear strength of rock variation with confining pressure obtained by triaxial tests, a new non-linear failure strength criterion for intact rock is developed on the basis of the peak value of deviatoric stress.Compared to the test data of 15 kinds of rocks, the average absolute error is only 2.964% by this strength criterion.All the regression coefficient R² of this strength criterion are larger than 0.96 for the No.1-15 rock.It shows that this strength criterion can well predict the triaxial test strength for different types of rocks with a universal applicability.This strength criterion has a slightly higher predicting accuracy than the exponential criterion regarded as an outstanding criterion in rock engineering.The predicting accuracy of this strength criterion is higher than Hoek-Brown (H-B) criterion, modified Hoek-Brown (MH-B) criterion and modified Mohr-Coulomb MM-Ccriterion.This criterion overcomes the limitations of the H-B criterion with larger deviation comparing with test data under higher confining pressure, and avoids the defect that MH-B criterion and MM-C criterion hold a constant after the confining pressure reaching uniaxial compressive strength σ_c.In addition, the relationship is established between the parameters of this criterion (k, a and m) and the parameters of Mohr-Coulomb criterion (cohesion c and internal friction angle φ).The instantaneous cohesion of rock increas with confining pressure, and finally increases to 0.5(k+1)σ_c.The instantaneous internal friction angle decreas as confining pressure increases, and gradually decreases to zero.The internal friction angle decreases to zero while the cohesion increases to the maximum value of 0.5(k+1)σ_c.For this strength criterion, the maximum value of rock deviatoric stress depends on the parameter k and uniaxial compressive strengthσ_c, and the increase magnitude of rock triaxial strength with confining pressure at initial section depends on the parameters value of a and m.Both parameters k and m have larger range of values, where k > 0 and m > 1.0.The value a is greater than 0 and less than 1.0, which is relatively centralized.In order to be convenient for calculation, a=0.95 is feasible.