Based on Timosheko-Mindlin kinematic hypotheses and Hamilton's principle a system of equations of motion is derived for geometrically nonlinear behavior of generally lamineted cylindrical thick panels of geometric initial imperfections. The variation of rotational stiffness is assumed to be identical along opposite edges. A solution for nonlinear vibratin of these panels is formulated by use of a muliti-mode approach. The boundary condilion for the varying rotational siiffness is satisfied by replacemnent of the edge bending moments by an equivalent lateral pressure near the paneldeges as in a previous work. The Galerkin procedure furnishes an infunite set of equations for time-dependent coefficients which is solved by the method of harmonic balance. Int the post-buckling case the set of time equations reduces to algebraic equations. Numericall results in nonlinear vibratio and post-buckling are presesnted gruphically for different parameters and compared with avalible data.