An etching process method is provided that includes outputting a first high frequency power from a first high frequency power supply in a cryogenic temperature environment where the temperature of a substrate is controlled to be less than or equal to −35° C., supplying a sulfur fluoride-containing gas and a hydrogen-containing gas, generating a plasma from the supplied sulfur fluoride-containing gas and hydrogen-containing gas, and etching a laminated film made up of laminated layers of silicon-containing films having different compositions with the generated plasma.