Abstract: The shear strength reduction finite element method as a recent development has been widely adopted for geotechnical stability analysis such as the slope analysis. In the shear strength reduction finite element method, however, the commonly used bracketing and bisection search algorithm for the safety factor may not be effective. To efficiently conduct the shear strength reduction finite element method, a bracketing and a-section search algorithm is proposed from the statistical point of view. Numerical simulations of 3D slope examples and some other examples show that compared with the commonly adopted search algorithms, the new a-section search algorithm is generally more efficient in the advised a range.