In the present work the buckling and postbuckling behavior of laminated cylindrical shells under axial compression and lateral pressure loading are investigated. A nonlinear theory for thin cylinders incorporating the effects of transverse shear deformation is employed. A modal solution based on the Koiter theory is utilized to derive the nonlinear equilibrium equations for the postcritical behavior of the shell. The Rayleigh Ritz method is used to obtain analytical solutions for the critical load through algebraic routines written in Maple. Prebuckling and postbuckling equations are also solved by using symbolic computation. The influence played by geometrical parameters of the cylinder and physical parameters of the laminate (i.e. fiber orientation of each lamina, material properties and number of layers) on the critical and postcritical behavior of the shell is examined. It is noticed that the stability of shells is highly dependent on laminate characteristics and, from these observations, it is concluded that specific configurations of laminates should be designed for each kind of application.