An etching process method is provided that includes outputting a first high frequency power of a first frequency from a first high frequency power supply, and outputting a second high frequency power of a second frequency, which is lower than the first high frequency, from a second high frequency power supply in an cryogenic temperature environment where a substrate temperature is controlled to be less than or equal to −35° C.; generating a plasma by adding a hydrocarbon gas containing at least 3 carbon atoms to an etching gas containing carbon, hydrogen, and fluorine; and etching a silicon oxide film or a laminated film made up of laminated layers of silicon-containing films having different compositions using the generated plasma.