A zig-zag plate model with variable kinematics and fixed degrees of freedom recently developed by the authors is applied to study indentation of sandwiches with honeycomb/foam core, with the aim of reducing the computational burden. This model, which a priori fulfils the stresses and displacements continuity requirements, has a hierarchic representation of displacements, but just five degrees of freedom. The core crushing behaviour is determined apart once at a time in order to account for the variable elastic properties of the core during the structural analysis. Specifically, shell elements with elastic-plastic isotropic material are adopted to discretize the cellular structure and the faces, instead solid elements with nonlinear material behaviour are chosen to model foams. Once the properties of core are determined, the analysis is quickly carried out in closed form by the zig-zag model. As customarily, the onset of damage is determined using stress based criteria, while its growth is accurately and efficiently described using a mesoscale model. In this way, the degraded properties of the failed regions are evaluated with a physically based model, instead of guessing suited multiplication factors. The numerical results of simulations are shown to be in good agreement with experiments taken from the literature.