Abstract: On the basis of the nonlinear dynamical foundational equations, the big deflection equation and the nonlinear dynamic equation of the shallow spherical shells were established by the method of quasi-shells. Dimensionless quantity of shells with uniform thickness was introduced and simplified the foundational equations and the boundary conditions under the fixed boundary conditions. First the big deflection is taken as the initial imperfect of the system and a nonlinear dynamic differential equation including the second and third order is derived by the method of Galerkin. The critical conditions of that chaos motion are given by solution the Melnikov function. Using the digital simulation plotted the plane phase and it approved existence of the chaotic motion and controlled the chaos。 Finally, it is found that the natural frequency of shallow reticulated spherical shells considering initial imperfect becomes bigger and the critical value of chaotic motion is smaller.