A method for making foam structures suitable for use as mechanical energy absorbers, structural members, filters, catalyst carriers or the like. A composite rod (114) comprising an outer shell and an inner core is formed of respective mixtures of powders. The mixture for the outer shell comprises a sinterable powdered structural material (101) such as ceramics, metals, intermetallics, and a powdered binder (102) such as paraffin, wax or polymer. The inner core comprises a powdered channel-forming filler material (108) such as melamine or polymers, or soluble inorganic compounds or a metal that can differentially be removed from the structural material of the shell. The composite rod (114) may be formed by extrusion. The composite rod (114) is sectioned into a plurality of composite rod segments of predetermined length and a plurality of these segments is assembled in randomly oriented relationship to one another. The assemblage of rod segments is then consolidated, and the binder and filler are then removed, as by heating. The remaining structure of the outer shells, comprised of ceramic or metal, as the case may be, is then sintered to produce the foam structure. In certain embodiments, the material of the inner core may be removed by heating it in the course of heating the structure to perform the sintering step. In other embodiments, the binder and/or filler material may be removed by means of a suitable solvent.