In the present investigation nonlinear static analysis of thin axisymmetric circular plates, annular plates and shallow spherical shells resting on linear elastic Winkler-Pasternak foundation under uniformly distributed normal loads, has been carried out. Donnell-type governing differential equations expressed in terms of normal displacement and stress function have been employed and solved using Chebyshev series. A convergence study for Chebyshev series has been conducted. The influence of foundation stiffness parameters (K and G ) on the response of circular plates, annulus and spherical shells has been studied for both the clamped and simply supported immovable edge conditions. A few typical snap-through results for shells are also included.