Abstract: By using the method of quasi-shells,the nonlinear dynamical equations are established for three-dimensional shallow spherical shellswith circular bottom based on the nonlinear dynamical equationsfor circular reticulated structures with three-dimensional grids.The foundational equations and the boundary conditions are simplified byintroducing dimensionless quantities, and a nonlineardifferential equation of the third order is derivedunder the boundary conditions of fixed edges by using Galerkin method. In orderto obtain the Melnikov function, the free oscillation equation of a kind ofnonlinear dynamics system is solved, and then the exact solution to the problem isobtained. The stability is discussedon the condition of no external excitation. The conditions for chaoticmotion are given by solving for the Melnikov function underexternal excitations. Existence of the chaotic motion is proved bynumerical simulation and the phase planes are plotted.