An accurate discrete model is presented here for the dynamics of simply supported web-core sandwich plates using the elasticity approach. By modelling the face-plates as 3D solids and the core webs using a plane stress idealization for transverse bending and classical one-dimensional models for lateral bending and torsion, the non-classical effects of transverse shear deformation, thickness-stretch and rotary inertia are completely accounted for in both, the face platesand webs. Vibrational frequency results obtained using this model are used to highlight the errors of the commonly used model based on the classical Kirchhoff hypothesis for the face-plates, indicating the importance of using refined theories for modelling the face-plates.