Abstract: In this paper, we use the method of mixed-type series to derive the analytical solutions of cylindrical shell, which is simply supported along the transverse edges and subjected to the local vertical loads, and give the analytical expressions of the solutions for this kind of shell under five types of local vertical loading.A numerical example for a cylindrical shell roof, which is simply supported along the trans verse edges and is free along the longitudinal edges, is given in this paper and from the calculated results it may he seen that the convergence of the solutions is considerably satisfactory.Using the solutions of this paper, we can deal with some practical problems of underground structure.

Key words: TCP system, stability, local Hopf bifurcation, global Hopf bifurcation, periodic solution