The invention relates to an assembly and a method for manufacturing a green tire and/or a green air spring. The device comprises a template having a shaping surface (2) for placing a tire component thereon comprising a layer of unvulcanized rubber for the green tire and/or green air spring. The shaping surface (2) is provided with an attachment surface (9) for at least temporarily retaining at least a leading section of the tire component. The attachment surface (9) comprises a number of adhering surface sections (3) with non-adhering surface sections (4) placed in between them, wherein the non-adhering surface sections (4) are at least partially receded with respect to the adhering surface sections (3). In one embodiment the attachment surface (9) comprises a substantially saw-tooth-shaped cross-section.