A series of experimental investigations and numerical analyses is presented into the compression response, and subsequent failure modes in corrugated-core sandwich panels based on an aluminium alloy, a glass fibre reinforced plastic (GFRP) and a carbon fibre reinforced plastic (CFRP). The corrugated-cores were fabricated using a hot press moulding technique and then bonded to face sheets based on the same material, to produce a range of lightweight sandwich panels. The role of the number of unit cells and the thickness of the cell walls in determining the overall deformation and local collapse behaviour of the panels is investigated. The experiments also provide an insight into the post-failure response of the sandwich panels. The results are compared with the numerical predictions offered by a finite element analysis (FEA) as well as those associated with an analytical model. Buckling of the cell walls has been found to be initial failure mode in these corrugated systems. Continued loading resulted in fracture of the cell walls, localised delamination as well as debonding between the skins and the core. The predictions of the FEA generally show reasonably good agreement with the experimental measurements. Finally, the specific compressive properties of the corrugated structures have been compared to those of other core materials where evidence suggests that these systems compare favourably with their more conventional counterparts.