A consistent higher-order theory is presented for static deformation and stress analysis of cross-ply thick laminates. Emphasis is placed on consistence with the 3-D boundary conditions and interlaminar stress continuity, exterior and interior, respectively, to the simply supported rectangular plate. All edges and lateral surfaces are considered stress-free, while surface traction and applied load equilibrium is maintained in the loading area. Individual layer displacement fields are expressed in terms of in-plane double Fourier series and cubic polynomials in thickness coordinates with continuity of interlaminar displacements and transverse stresses observed. A system of equations is derived with all these necessary conditions satisfied by means of the higher-order terms of the displacement fields in the extended Rayleigh-Ritz procedure. 3-D displacement and stress components, as compared well with exact solution cases available, can be found throughout the plate for 3-D analysis of localized damage. Thickness shrinking is noted with no mid-surface symmetry of stress distribution.