Stability analysis of engineering structures requires tracing equilibrium path of the structure when member’s buckling or material softening occurs. In nonlinear finite element analysis, the traditional Newton method fails at limit point and bifurcation point. The arc-length continuation method can overcome these numerical difficulties. To develop a nonlinear finite element code for stability analysis, the standard iteration formulation of Newton method is presented for the arc-length continuation method. Two practical formulations of the arc-length continuation method and their relationships with the standard form are also discussed. The applicability of the practical formulation is examined by the finite element analysis of stability for a slope.