Abstract: The geometrically nonlinear problem of laminated composite shells have received considerable attention in recent years.However, in the classical geometrically nonlinear theories of shells, the equations of inplane equilibrium have not involved the effect of dofermation.So they are not suitable for the case of relatively large deformation, at least they are not accurate. In this paper, starting from the three dimensional theory of nonlinear elasticity and taking into account of the effect of deformation in all equilibrium equations,we present a new geometrically nonlinear theory of shells which differs from classical theories according to scale-order analysis under the condition of small strains and moderate rotations.The governing equations of nonlinear analysis for orthotropic composite shallow cylindrical shells are derived by the same method in which the effect of transverse shear deformation is considered.The approximate solutions of nonlinear bending for orthotropic laminated composite cylindrical shells with all clamped edges are obtained by the perturbation method.The approximate solutions of nonlinear bending for orthotropic composite shallow cylindrical shells with all edges simply supported are also obtained by the Galerkin procedure, and the effect of transverse shear deformation is taken into account.