Based on von Kármán-Donnell kinematic assumptions for laminated shells, the non-linear vibration and postbuckling behaviour of unsymmetrically laminated cross-ply circular cylindrical shells with clamped and simply-supported ends are studied by a multi-mode approach. A solution is formulated and satisfies the associated compatibility equation and all boundary conditions. The transverse equation of motion is fulfilled by the Galerkin procedure. In the case of non-linear vibration problems, the solution is obtained by the method of harmonic balance. The effect of initial imperfection is also included. Results in non-linear vibration and postbuckling are presented for different amplitudes of initial imperfection and four sets of boundary conditions. Present results are compared with available data. © 1988.