Summary: A solid shell element model with six degrees of freedom per node is applied to buckling and postbuckling analysis of geometrically nonlinear shell structures. The present model allows changes in the thickness direction and does not require rotational angles or parameters for the description of the kinematics of deformation. The finite element model is constructed based on the assumed strain formulation in which an assumed strain field is chosen to prevent locking while maintaining kinematic stability. Numerical results show that the present model allows large increments in the iterative solution scheme for pre- and postbuckling analysis. In particular, it appears that the model provides a means to pinpoint a bifurcation point on the geometrically nonlinear deformation path.