A rigid polymer porous material sheet is produced by feeding a slurry of polymer mixture comprising ultrafine polyvinylchloride particle, non-phthalate plasticizer, foaming agent and thermal stabilizer, polymer chips, fillers and fire retardant chemicals into a heated mold and pressing the mixture with high applied pressure. The temperature of the mold is below 190° C. to soften the polymer mixture and decompose the foaming agent forming the closed cell polyvinylchloride foam with 10 to 40% density with closed air cells. The thermal resistance of the rigid polymer porous sheet and sound attenuation properties are significantly improved. The rigid polymer porous sheet can be bent at sharp angles without crack formation facilitating its use as wall boards. The sheets produced may be embossed or molded to produce decoration boards, advertising boards, cabinet doors and furniture with decorative features. They can also be used in aeronautical applications as acoustic thermal insulation systems.