Abstract This paper presents an original hyperbolic sine shear deformation theory for the bending and free vibration analysis of functionally graded plates. The theory accounts for through-the-thickness deformations. Equations of motion and boundary conditions are obtained using Carrera’s Unified Formulation and further interpolated by collocation with radial basis functions. The efficiency of the present approach combining the new theory with this meshless technique is demonstrated in several numerical examples, for the static and free vibration analysis of functionally graded plates. Excellent agreement for simply-supported plates with other literature results has been found.