The invention comprises a fully continuous process for shaping a high internal phase emulsion (HIPE) with a polymerizable continuous phase into dry foam, comprising 1) providing a high internal phase emulsion (HIPE) comprising (a) at least 70 percent by volume of an eternal phase comprising one or more polymerizable monomer; (b) a surfactant in an amount effective to produce a high internal phase emulsion; and (c) an internal phase; 20 depositing the emulsion onto a lower moving support substrate; 3) leveling the emulsion to a desired thickness above the support substrate; 4) polymerizing the monomers by running the emulsion and the lower moving support substrate through a heating zone for a time sufficient to polymerize at least 75% of the monomer in the HIPE by the end of the heating zone; and 5) drying the polymerized HIPE in a drying zone for a time sufficient to produce a foam having greater than 50% of the internal phase removed.