Described is an embossing apparatus for transferring a transfer layer of an embossing film on to a substrate body which is stable in respect of shape. The embossing station has two mutually spaced support rollers and a deflection roller around which runs an embossing belt. An embossing section of the embossing belt is defined by the support rollers. Provided in the proximity of the embossing station in parallel relationship with the embossing section is a transport device which is provided for transporting the substrate body to be embossed. The embossing belt and the transport device are driven simultaneously at the same advance speed.