To inexpensively produce foams of high melting materials (metals and ceramics) having excellent lightness in weight, air permeability and filtration characteristic and directional pores.

Metals or ceramics are melted in a melting furnace to obtain molten metal. Gases consisting of at least one kind of gases among gaseous H, N and O, are applied to this molten metal and the total pressure 1 to 500atm of the gases is applied thereto to dissolve the gases. Casting molds are preheated to a range of the respective. m.p. of the metals or ceramics ±50°C. While the total pressure of the gases applied to the molten metal is maintained, the molten metal is poured into the preheated casting molds. While the total pressure of the gases applied to the molten metal is maintained, the heat extraction from the upper surface and flanks of the casting molds is prevented and the heat is extracted from the lower surface alone to allow the molten metal to solidify. The molten metal is unidirectionally solidified to the foam which extends upward, has the directional pores of a minor diameter of 5μm to 10mm and porosity of 50 to 98%. Further, fine particles to constitute the nuclei for foaming are added to the molten metal.