An accurate discrete model is presented here for the analysis of simply supported web-core sandwich plates. In this model, the face plates are analysed using the equations of 3D elasticity and for the webs a plane stress idealization is used to model the kinematics of transverse bending while simple one-dimensional classical models are employed for lateral bending and torsion. Thus, this model accounts for the non-classical effects of transverse shear deformation and transverse thickness-stretch in the face-plates and the webs. It is shown that this model is capable of accurately capturing the effects of secondary local bending of the face-plates between the webs on the displacement and stress fields. Results obtained by this rigorous approach are used to highlight the errors of the commonly used model based on the classical hairbrush hypothesis for the face-plates. © 2015, © The Author(s) 2015.