<p>A mattress system providing a sleeping surface is described and includes a mattress and mattress support each having a honeycomb core formed of undulated strips of resilient thermoplastic material, thermal compression bonded together and expanded to form cell walls defining a plurality of contiguous regularly shaped cells. The honeycomb cores have a top face and a bottom face which have been subjected to a thermal compression planarizing deformation. A first facing sheet of resilient thermoplastic material is bonded to the top face of each honeycomb core, and a second facing sheet of resilient thermoplastic material is bonded to the bottom face of each honeycomb core. The mattress support is configured to support the mattress and a human body positioned on top of the mattress.</p>