Previous attempts to analyze indentation of sandwich panels have been based on small deflection theory and an assumed elastic core behaviour. The agreement with experiments was poor. The present work includes core crushing and large deflections of the face sheets in a simplified model of sandwich contact indentation. The model assumes transverse isotropy with respect to the load axis and is based on an infinite, elastic face sheet on a core bonded to a rigid foundation. The core is assumed to be elastic in tension and elastic-ideally plastic in compression. After initiation of core yielding the problem is separated in two regions. In the inner, plastic region, the core has yielded and exert a constant reactive pressure on the face sheet. In the outer region the core acts as an elastic foundation. The plastic radius is found by matching boundary conditions for the two regions.The outer region is modeled as a plate on an elastic foundation. The inner region is modeled using three different approaches. For small deflections classical plate theory with shear corrections is used. For intermediate deflections an upper limit of the contact force is given by first order large deflection plate theory and a lower limit by small deflection plate theory. The asymptotic behaviour at large deflections is given by an approximate solution based on membrane theory. The three solutions, which all require iteration, have been put in dimensionless form and tabulated. The approach due to Hertzian contact has been included in the plate solution. Bounds have been given for the residual indentation after unloading. Approximate expressions are given for analysis of orthotropic face sheets.Good agreement with experiments was found for sandwich panels of different materials and thickness. The often observed, approximately linear, load-indentation relation is found to be the combined effect of softening due to core crushing and stiffening due to face sheet membrane effects. A limited parametric study indicates a strong influence of the core yield stress and the face sheet properties, and a relatively weak influence of the thickness and elastic properties of the core. The local indentation model may be used in a global impact model to predict impact response of sandwich panels, or as a starting point for more detailed stress analyses for prediction of damage due to impact and contact loads.