Abstract：Based on limit equilibrium theory，a basic coordinate system and an auxiliary coordinate system are set up according to the size and geometrical relationship of slope. By virtue of the basic coordinate system，firstly，the function relations are deduced between the geometrical control parameter of slip surface and the center coordinate of circular slip surface. Then，the function relations are deduced between each variable in the safety factor expression and the center coordinate of circular slip surface. Thereby，the function relations are derived between the geometrical control parameter of slip surface and the safety factor of slope. By moving the auxiliary coordinate system along the slope surface，and controlling the position and geometrical parameter of slip surface，the arbitrary potential slip surface is generated to calculate the safety factor，and further the minimum safety factor and the most dangerous slip surface are determined. This method is suitable for the determination of the critical surface in multi-step slope，and it can avoid inaccuracy caused by using empirical formula to determine the search region of slip surface center，and solve the difficult problem to determine the critical slip surface in multi-step slope. It is a new computer search model to solve the stability of multi-step slope. Finally，a program is compiled，and a practical example is calculated and analyzed.
