Lightweight, open-celled foams and honeycombs can exhibit deformation localization during static crushing as a result of buckling and plastic collapse of cell walls. Localization of deformation is a manifestation of strain-softening behavior that limits transmitted forces through these shock mitigating materials. Collision tests on two-dimensional cellular solids with strain-softening behavior reveal that with some microstructures, strain-rate effects can stabilize less compliant modes of deformation. When stabilization occurs, it amplifies the intensity of transmitted shocks.