Technological advances in recent years have enabled an increasing complexity in the design of structural elements, such as plates. This poses challenges in the numerical analysis, particularly during the meshing process. Original limitations to triangular and quadrilateral elements often necessitate user interventions for the mesh generation. In this context, polygonal element formulations, such as the Scaled Boundary Finite Element Method, prove beneficial by enabling arbitrary numbers of nodes per element and thereby simplifying the inclusion of local mesh refinements. Focusing on thin plate structures, a crucial aspect lies in the choice of plate theory. The earliest plate formulations were based on Kirchhoff-Love assumptions, which impose a C1-continuity requirement for shape functions. In contrast, Reissner–Mindlin formulations account for shear deformations and thus have a lower continuity requirement. However, while low-order Reissner–Mindlin formulations offer computational efficiency, they face issues with transverse shear locking. Remedies, such as assumed natural strains must be incorporated to reduce the overestimation of shear stiffness in the thin plate limit. This contribution focuses on a polygonal Reissner–Mindlin plate formulation within the framework of Scaled Boundary Finite Element Methods. In difference to the original semi-analytical approach, linear shape functions are introduced in both scaling and radial direction, resulting in a fully discretized and low-order element formulation. Transverse shear locking is addressed through an assumed natural strain approach tailored for application at section level of polygonal scaled boundary finite elements. Through the additional introduction of a two-field formulation, the incorporation of three dimensional- laws is enabled, where the plane stress assumption is fulfilled in a weak sense.