Abstract: During the melt spinning process for producing metal foils having an amorphous structure, molten metal is cast through a slot-like nozzle onto a surface or wall which is rapidly moved past the nozzle. A particularly rapid quenching and cooling rate of the solidifying melt is achieved by providing cooling support elements which are supplied with a cooling pressure medium, on one side of the moved surface or wall and which aide is located opposite to or remote from the nozzle. Advantageously, the surface or wall is constructed as a thin-walled cylindrical shell or tube which is elastically deformable to some extent. In its shell interior, there are provided a number of rows of cooling support elements which may be controlled by thickness sensors and temperature profile sensors. There is thus rendered possible, the continuous production of amorphous metal foils.