Abstract: In this paper some basic problems in the analysis of nonlinear instability for multilayered composite cylindrical shells are discussed. These problems are: the influence of initial imperfections and geometrical nonlinearity of shells; the effects of physical nonlinearity caused by the material nonlinearities of shear modulas; the influence of transverse shearing deformation and the effect of prebuckling deformations on buckling and postbuckling behavior of laminated composite cylindrical shells under various boundary conditions. All of these influences are studied under various loading conditions: e.g.axial compression, hydrostatic pressure and torsion. The interaction of these influences is an important and complicated problem.This paper is a report for the sythetic analysis of these influences that based on a series of our investigated results in the recent years.