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It is necessary to select an instability criterion for the material point strength reduction method (SRMPM) to solve the slope safety factor (Fs), and there are some differences in the obtained Fs values with different instability criteria. To examine the rationality and applicability of the four common instability criteria (i.e., calculation nonconvergence, displacement mutation of the feature point, transfixion of the plastic zone and the limit value), this paper uses the SRMPM to analyse the stability of two slope examples. The Fs obtained by the Spencer limit equilibrium method (LEM) is taken as a reference to further verify the rationality and accuracy of the results. The results show that ① the material point calculation is convergent, so the calculation nonconvergence cannot be used as the slope instability criterion; ② when the displacement mutation of the feature is regarded as the criterion of slope instability, the Fs is basically consistent with the LEM, so the displacement mutation of the feature point can be used as the slope instability criterion; and ③ the limit value and the transfixion of the plastic zone cannot be used alone as the slope instability criterion.