This paper presented a meshless local Petrov-Galerkin method based on the natural neighbour interpolation for a plate described by the Reissner-Mindlin theory. The natural neighbour interpolation shape functions have Kronecker Delta function property, which facilitates the imposition of essential boundary conditions. The local weak forms of the equilibrium equations and the boundary conditions are satisfied in local polygonal sub-domains in the mean surface of the plate. These sub-domains were constructed with Delaunay tessellations and domain integrals were evaluated over included Delaunay triangles by using the Gaussian quadrature scheme. The present method combines the advantage of easy imposition of essential boundary conditions of NEM with some prominent features of the MLPG. The numerical results have shown that the proposed method is easy to implement and very effective for these problems.