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Five multiparameter empirical criteria were exclusively evaluated by comparing them with the strength data covering various stress conditions to find out which failure criterion best fits the test data and describes the mechanical behavior of the salt rock sequence (halite, bedded composite specimens and anhydrite interlayers). Full-scale comparison of all criteria for the three rock types was conducted based on five standard statistics calculated from least squares curve-fitting, which measures both the goodness of fitting and the quality of future prediction. The results indicate that all five nonlinear criteria with a basic power form are efficient in predicting the strength trend in the low tension area as well as in the high compression area of the soft rocks. The parameters obtained for the bedded rock salt are somewhat in the ones for the pure rocks and are even closer to those obtained for the halite.The generalized Hoek-Brown criterion is proven to perform best to two rock strength data followed by one for the Bieniawski empirical criterion, thus is the best candidate for the analysis of the salt rock. The Sheorey empirical criterion consistently achieves an intermediate performance for all the three rocks. It seems that the superiority of the poly-axiai criteria (the Mogi 1967 criterion and the N-type criterion) over the former three triaxial criteria no longer exists when applied to the conventional triaxial strength data.Besides, the method of tension cut-off was proposed to solve the ambiguity problem of the two poly-axial criteria in the tension field in the plane of the major (σ1) and minor principal stress (σ3).