To water-treat a foamable thermoplastic resin sheet with a lengthy lap winding, to crosslinking react the sheet at a homogeneously highly treating speed, and to improve safety of its operation by providing a conveying rail inclined to convey the sheet lap winding in a water-treating chamber inclined at a winding core of the winding of the sheet to a horizontal surface.

Steams are supplied from a steam supply port 15a passing through a cover 21 and a steam supply port 15b passing through an opposed wall toward both side faces of a foamable thermoplastic resin sheet lap winding W, and a crosslinking reaction is started. The steam full filling a water-treating chamber in the pressure container 1 is quickly water-treated through air gaps of foamable thermoplatic resin particles dispersively disposed uniformly on a resin sheet, and uniformly, efficiently completed in its crosslinking reaction. The winding W completed in the reaction is moved on an inclined rail 13 by opening the cover 21, and delivered out of a pressure container body while dripping condensed steam and adhered water. Thus, the winding W can be crosslinking reacted at a homogeneously high treating speed, projection of hot water is prevented, thereby improving its safety.