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This paper develops a nonlinear shear-strength reduction technique for analyzing the stability of uniform slopes with the general nonlinear failure criterion. To incorporate the nonlinear power-law failure criterion into the finite-element slope stability analysis with the shear-strength reduction method (SSR-FEM), a general tangential approach is employed to obtain the instantaneous cohesive strength and internal friction angle from the power-law failure criterion iteratively. Therefore, the shear strength of the power-law criterion can be expressed by the instantaneous Mohr–Coulomb (MC) parameters related to stress within the slope soil. By this way, it is possible to use the linear MC failure criterion for the nonlinear slope stability analysis based on the conventional SSR-FEM. The proposed approach is applied to three typical examples including a homogenous 2D slope, a homogenous 3D slope, and a high rockfill embankment slope. The results show that the nonlinear shear-strength reduction technique presented in this paper can guarantee the accuracy and feasibility to determine the factor of safety (FOS) and provide an alternative way for stability analysis of simple uniform cohesive slopes with a general power-law criterion. [ABSTRACT FROM AUTHOR]