Abstract: Based on nonlinear dynamic theory of thin shells and the basic large deflection equations of the shallow reticulated spherical thin shells, regarding large deflection as the initial deflection, the basic nonlinear dynamic equations are established by using the modified iteration method to obtain the analytical solution of quadratic approximation under the boundary conditions of clamped edges. The tension is obtained according to the displacement model that satisfies the same boundary conditions. The equation of the balanced surface is obtained by set the first variation of the dynamic potential to be zero. Then, the systems of equations of the corresponding bifurcation point set are given in terms of catastrophic theory and the whole stability of the shallow thin spherical shells is discussed. In addition, the sketch map of the corresponding bifurcation point set of the balanced surface is also given in this paper.