In this book, refined member calculation model is established by which the possible buckle-straighten processes of the members and the form-disappear processes of the plastic hinges of the structure under earthquakes can be simulated. Mechanical calculation model for welded hollow spherical joint is established by which the repeated loading-unloading processes and failure process of the joint under seismic excitations can be simulated. Results of parametric analyses of single layer lattice shells under severe earthquake indicate that dynamic damage for spherical lattice shell is determined by structural instability resulted from member buckling; and for cylindrical lattice shell, it is determined by the combined effect of structural instability and the change of structural topology that resulted from member buckling and joint fractures. The bearing capacity of initial imperfect lattice shell is also discussed. A new method to calculate the design bearing capacity of the initial imperfect lattice shell at a uniform probability level is proposed, and its error expression at certain confidence level is derived.