<p>To capture the tensile–shear composite failure characteristics of prestressed anchor cables in slopes, this study derived a three-dimension (3D) calculation model for the shear resistance effects of prestressed anchor cables with different anchorage angles, prestress levels, and steel strand material utilization coefficients through theoretical analysis. Based on this model, a 3D nonlinear optimization method for slope stability analysis considering the shear resistance of prestressed anchor cables was constructed, with the maximization of the slope safety factor as the objective function and force–moment equilibrium as the primary constraints. And an efficient bisection iterative optimization solving algorithm based on logical judgment was proposed, which greatly improves optimization efficiency and ensures absolute convergence. Verification through model tests confirmed the validation of the proposed shear resistance effect calculation model. Analysis of engineering cases demonstrated that commonly used methods significantly underestimate the reinforcement effect of prestressed anchor cables, while the proposed method can reduce the amount of support structures by 50% with the inurement of engineering safety.</p>