It is necessary to obtain the critical slip surface in soil slope stability analysis. However

the existing analysis methods can not ensure the accuracy; and some analysis methods may fall into local minimum trap in the process of calculation. In order to obtain a non-spherical critical slip surface that is most similar with the actual slip surface

an alternating variable local gradient method is proposed based on univariate method and steepest descent method. This method can break through the bottleneck of optimization method applied to slope stability analysis. At first

the initial critical ellipsoidal slip surface of slope can be determined by Spencer limit equilibrium method and the grid search method (or any other method to determine the critical slip surface). Then

several nodes are arranged on the slip surface as variables; the objective function is an equation of safety factor Fs versus space node coordinates Zi; to make the value of objective function decrease fast

each node is optimized according to the negative gradient direction in every cycle. When the result meets the accuracy requirements

the non-spherical critical slip surface of the three-dimensional soil slope is obtained. Finally

this method is proved to be feasible and accurate by two examples.