Based on the theory of Lematire's equivalent strain of the damage, taking into account the damage of bars of the shallow reticulated spherical shell, and according to nonlinear dynamical theory of thin shells, the nonlinear dynamical equations and the consistency equation of the shallow reticulated shells with damage were obtained by quasi-shell method. Under the fixed and clamped boundary conditions, a nonlinear differential oscillation equation with quadric and cubic items was presented by the Galerkin method, and a nonlinear free oscillation equation of the shallow reticulated shells with damage was solved. Then the bifurcation of the system was discussed by Floquet exponent method, and the state of the equilibrium point was given. Lastly the bifurcation map and the relative position map of the equilibrium point were plotted by numerical emulation under the different damage state. It is founded that the damage of the bars of the shells greatly impacts on the state of the equilibrium point.