The paper is dedicated to improvement of plate theory in order to take into account forces, moments and bimoments, generated by nonlinear law of displacement distribution in plate cross-sections. Integral correlations for defining forces, moments and bimoments were given. The developed bimoment plate theory is described with two independent two-dimensional systems with nine equations in each. On each edge of plate nine boundary conditions were set. The approach to building the bimoment theory is based on the Hook law, three-dimensional equations of elasticity and decomposition of displacements in Maclaurin series. As an example, the solution of the problem of thick orthotropic plate buckling under action of transverse harmonic sinusoidal load was described. Numerical results were obtained for displacement, force, moments, bimoments and stresses, accompanied by analysis.