The invention relates to a device (01) having at least two tool parts (03, 53, 63) that are separable at a parting face, wherein the closed tool parts (03, 53, 63) form a mold cavity (02, 52), within which (02, 52) particulate plastic material can be foamed and/or expanded to produce foamed molded parts. According to the invention, in particular to reduce the energy consumption, the tool wall forming the mold cavity (02, 52) is formed at least in sections by a multilayer structure (06, 56, 65) having a thin inner layer that is mechanically supported by a support element.