Abstract: In this two part paper, theory and numerical methods are proposed on nonlinear bifurcation problem in structure stability in the first part. A general FEM code was improved by those methods. In part Ⅱ, the snap-through of a square plate with all edges clamped, which is loaded by uniaxial compression, is simulated. The solution path on post-buckling behavior of square plates is traced globally by this FEM code. The stable equilibrium can simulate the whole process of snap-through of the square plate during loading and unloading. The phenomenon, that deflection direction of plate in the first buckling mode during loading is opposite to deflection direction of plate in the first buckling mode during unloading, is demonstrated by the numerical results in this paper. Also numerical results in this paper agree well with available experimental data.