The finite element modelling of elasto-static plate bending problems is developed with quadrilateral hybrid elements based on a simple 3D extension of Reissner-Mindlin theory. The hybrid elements are formulated with internal fields of statically admissible stresses, and boundary fields of displacement which are defined independently for each side and are generally non-conforming. These elements enable a strong form of equilibrium to be satisfied, and a hierarchical form of a flexibility method is presented for the analysis of a system of elements. Equations are solved in a block form of a Gauss-Seidel iterative method. A method for recovering a fully conforming displacement field is proposed. A numerical example of a square plate is presented with results for convergence and non-conforming side displacements.

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