An optimum reticulated shell structure is selected and its dynamic properties are analyzed. In this paper analyses the dynamic feature and gains the elementary parameters from the analysis of free vibration. The frequencies and modes are compared by two finite element methods. The paper analyzes the dynamic responses of the reticulated shell structure subjected to two-dimensional and three-dimensional earthquake waves respectively. Simultaneously analyses the linear，geometric nonlinear and both geometric and material nonlinear dynamic responses in two situations. The nodal displacements and stresses of members are compared and analyzed. The characteristics of elastoplastic seismic responses of the structure are revealed and the basic rules are obtained.