Abstract: Using the method of simulated shell, non-linear dynamic differential equation of three-dimensional single-layer shallow lattice shell with equilateral triangle mesh is established. The lateral displacementof lattice shell is obtained by separation of variables for fixed boundary condition. The stretching force is obtained from the compatibility equation. A non-linear differential equation with quadratic and cubic terms is established by Galerkin method. The system has three equilibrium points on the condition that external excitation is ignored. Stability close to the null equilibrium point is discussed by the Floquet exponent. In order to study the chaos motion, non-linear free vibration equation of this dynamic system is solved with the given initial conditions. An accurate solution of the non-linear free vibration system is obtained. This makes Melnikov founction obtainable. Melnikov founction is obtained by theory of residuals, and the critical condition is also obtained. Numerial-graphic method and Poincare map confirm the existence of chaos.