For homogeneous plates, the highest order term of transverse shear and normal stresses is of second order in thickness. To take this effect into account, we show that the thickness-wise expansion of the potential energy must be truncated at least from fifth order in thickness. The equilibrium equations imply local constraints on the through-thickness derivatives of the zeroth-order displacement field. These lead to an analytical expression for two-dimensional potential energy in terms of the zeroth-order displacement field and its derivatives, which include non-standard shearing and transverse normal energies and coupled stretching–shearing, bending–shearing and stretching–transverse normal energies. As a consequence, this potential energy satisfies the stability condition of Legendre–Hadamard, which is necessary for the existence of a minimizer.