By folding a thin flat sheet with periodically set slits or punched out portions into the third dimension, ultra-lightweight strong and functional core models are newly devised. The basic idea of this modeling arises from the application of origami technique to engineering. Based on the space filling models, fundamental flat cores and skew type sponge cores have been newly developed. By applying these models, such modified core models as curved cores and 3D honeycomb core are newly devised.