This paper presents an experimental investigation of compression on pristine specimens and the compression after impact (CAI) response of wood-based sandwich structures. Nine different types of sandwiches, made with plywood core and different aluminum or composite (carbon or glass or flax fiber) skins, are studied. Impact energy levels were fixed at 5 J, 10 J and 15 J in order to create significant defects. Failure modes and damage scenarios are analyzed. The influence of different skins with plywood core is explained in terms of residual strength, residual stiffness, and specific properties. It is shown that this type of structure exhibits very interesting compression properties in terms of specific strength, which is superior to a reference sandwich used for aircraft flooring, and in terms of behavior, with large plateau areas that can be useful for crash issues.