The paper gives an overview of issues relating to the characterisation of the progressive collapse of core cellular materials used in sandwich construction. The specific structural application addressed is foreign object impact, and in this case the core cellular material is subject to multi‐axial stresses, progressive collapse and possible rupture. The paper gives an overview of various theoretical and modelling issues, which are then related to experimental materials and structural tests for model development, calibration and validation. Most discussion concerns polymeric crushable foam, metal foam and metallic lattice structures.