The paper presents a new constitutive model for closed-cell polymeric foams. The model is of the microplane type. In this model, the constitutive law is characterized in terms of vectors rather then tensors. The conceptual simplicity of this ‘first-principles’ approach makes it possible to base the model more directly on the physical phenomena occurring in the microstructure, in this case the elastic bending of the cells idealized as spheres in contact. The model is then employed in a finite element analysis of three point bending tests of sandwich beams failing by core indentation. Good agreement of the numerical results with the experimental observations is achieved. The softening and size effect engendered by the reduction of tangential bending stiffness due to the geometrically nonlinear effect of core indentation is discussed.