The Refined Zigzag Theory (RZT) belongs to the zigzag class of approximations for the analysis of laminated composite and sandwich structures. This paper presents the derivation of the non-linear equations of motion and consistent boundary conditions of RZT for multilayered plates. Subsequently, the equations are specialized to the linear boundary value problem of bending and the linear eigenvalue problems of free vibrations and buckling. In order to assess the accuracy of RZT, results concerning the static response, the free vibration frequencies and modal shapes, and the buckling loads of symmetric and un-symmetric sandwich plates, both simply supported and clamped and subjected to several loading conditions, are compared to the three-dimensional exact elasticity solution, high-fidelity FEM solutions, classical and zigzag theories, and accurate layer-wise models or solutions obtained in the open literature by means of other methods. The numerical investigation shows that RZT is highly accurate in predicting the static response, the natural frequencies and the buckling loads of sandwich plates without requiring any shear correction factors. In virtue of its accuracy and of the C⁰-continuity requirement for shape functions, RZT can be adopted to derive reliable and computationally efficient finite elements suited for large-scale analyses of sandwich structures.