In this paper, a novel analytical model for predicting the post-crushing compressive response of progressively crushable sandwich foam cores is presented. The calibration of the model is performed using experimental measurements obtained exclusively from standard monotonic compressive tests. Therefore, the need for performing time-consuming compressive tests including multiple unloading–reloading cycles is avoided. Model predictions have been validated against experimental measurements available for three different foam materials. The model is shown to accurately predict the thickness of the crushed material layer during progressive crushing and the residual after-crushing strain (with a maximum error of 12.1%). The proposed model is capable of predicting the residual after-crushing strain with a significantly smaller error (error-reduction over 56%) than existing models, whose calibrations require the same experimental measurements as the present model. The results presented in this work demonstrate the relevance of the proposed model for a damage-tolerant design of foam-cored composite sandwich structures.