AbstractTwo alternative hybrid‐stress based three‐dimensional elements are presented. These elements are intended for use in the analysis of thick plates for which the through‐thickness variation of displacement and stress may be of high order, and in which a single element is to be used through the thickness of the plate. For both elements, the displacement assumption allows for cubic through‐thickness variation in the inplane displacements, and quadratic through‐thickness variation for the transverse displacement. The elements differ in the stress assumption used. In the first element, the z variations in the stress components are chosen to be consistent with the z variations of the strain distribution calculated from the displacement assumption, and the traction boundary conditions at the upper and lower surfaces are satisfied in the weighted integral sense. In the second element, the z variations in the stress components are chosen to achieve consistency with respect to the equilibrium equations, and the traction‐free conditions at the upper and lower surface of the plate are satisfied exactly. The example problem of a semi‐infinite, simply‐supported thick plate under transverse sinusoidal loading is considered. Results obtained by using each of these elements are compared with available elasticity and approximate solutions, and an assessment of the relative merits and range of applicability of each