A supporting bed for supporting a stack of sheet material in a cutting machine of the type retaining the material by means of a vacuum applied from below the supporting bed is manufactured from a composite structure of starting material including individual layers of reticulated foam material separated by at least one layer of a hot melt adhesive web. The composite structure is compressed under heat and pressure so as to be permanently reduced to approximately 10-35% of its initial thickness. The degree of compression, the temperature and compression time, and the porosity of the retriculated polyurethane foam starting material are selected to provide particular airflow and firmness characteristics for the finished supporting bed.