A numerical model for the simulation of dynamic compression of a collapsible multilayer structure subjected to transient compressive excitation is described and tested. It is shown that impacts induce a chaotic collapse of crumple layers. The simulations predict shock pulses and intralaminar forces. Simulated shock pulses that a free-falling impactor is subjected to, and the corresponding animated deformation histories of the layers, are compared with the highspeed videography. Cushioning performance maps and shock response spectra maps obtained from the simulations are presented. The use of collapsible structures for cushioning applications is discussed.