<p>In this work, a polygonal Reissner–Mindlin plate element is presented. The formulation is based on a scaled boundary finite element method, where in contrast to the original semi-analytical approach, linear shape functions are introduced for the parametrization of the scaling and the radial direction. This yields a fully discretized formulation, which enables the use of non-star-convex-polygonal elements with an arbitrary number of edges, simplifying the meshing process. To address the common effect of transverse shear locking for low-order Reissner–Mindlin elements in the thin-plate limit, an assumed natural strain approach for application on the polygonal scaled boundary finite elements is derived. Further, a two-field variational formulation is introduced to incorporate three-dimensional material laws. Here the plane stress assumptions are enforced on the weak formulation, facilitating the use of material models defined in three-dimensional continuum while considering the effect of Poisson’s thickness locking. The effectiveness of the proposed formulation is demonstrated in various numerical examples.</p>