Geometrically non-linear composite shell element based on updated Lagrangian method is deveolped to study the buckling behavior. The element is capable of small strain and large displacement analysis with finite rotations. It has eight nodes with six degrees of freedom per node. Transverse shear deformation effects are included using a first order theory which allows modeling of relatively thick plates and shells. Birfucation and postbuckling analysis of the laminated plates and shells under axial compression are carried out using finite element method. Results showed that solutions by present formulation have very good agreement with references.