A postbuckling analysis is presented for a simply supported, composite laminated rectangular plate under uniaxial in-plane loading and resting on a two-parameter (Pasternak-type) elastic foundation. The analysis uses a perturbation technique to determine buckling loads and postbuckling equilibrium paths. The initial geometrical imperfection of the plate is taken into account. Numerical examples are presented that relate to the performances of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated rectangular plates. Typical results are presented in dimensionless graphical form.