an apparatus for producing a thermoplastic synthetic resin sheet or film has a casting mechanism having support rollers each mounted to undergo rotation about a corresponding rotational axis and one of which is mounted to undergo non - rotational displacement relative to the other support rollers . a casting sleeve is entrained around the support rollers for rotation therewith . a casting roller is mounted for undergoing rotation relative to the casting sleeve . a synthetic resin material is fed between opposite and confronting outer peripheral surfaces of the casting sleeve and the casting roller while rotating the casting sleeve and the casting roller and while effecting non - rotational displacement of one of the support rollers to holdingly press the synthetic resin material between the casting sleeve and the casting roller and thereby form the synthetic resin material into a thermoplastic synthetic resin sheet or film .