Well wall instability during production of bare-hole wells is mainly caused by changes in the perimeter stress state, and the rock damage criterion is a key factor in carrying out the prediction of well wall stability during production of bare-hole wells. Based on multi-axis rock mechanics tests, this paper compares and analyzes Mohr-Coulomb and Mogi-Coulomb prediction results under conventional tri-axial stress and true triaxial rock stress states, and also reveals the influence of intermediate principal stress coefficients and principal stress distribution characteristics on the applicability of rock strength criterion. It is found that the Mohr-Coulomb criterion neglects the influence of intermediate principal stresses, which causes the predicted rock strength values to be larger than the measured values; the prediction accuracy of the Mogi-Coulomb criterion is higher than that of the Mohr-Coulomb criterion in all the tri-axial stress states; the influence of intermediate principal stresses on rock strength prediction cannot be neglected, and the more uniform the distribution of principal stresses, the higher the accuracy of rock strength prediction. The more uniform the distribution of principal stresses, the higher the accuracy of rock strength prediction. This paper demonstrates that the prediction curves of Mogi-Coulomb criterion in conventional stress state also have better applicability in true tri-axial stress space, which promotes the further application of Mogi-Coulomb criterion in engineering applications and lays the foundation for theoretical research on wellbore safety evaluation during the production of drilling and bare borehole wells.