Method and apparatus for the continuous production of transparent films, sheets, or plates of high optical quality are disclosed. Material in liquid form flows onto a substrate comprising a plurality of discrete, distortion-free panels, disposed in end-to-end abutting relationship and moved continuously beneath a flow head from which the material flows onto the panels. The panels move on a conveyor system that progressively slows the speed of the plates, so that leading and trailing edges of successive panels abut to form a continuous surface as the panels pass beneath the flow head. Yieldable, elastic sealing strips are placed between the panels to form a part of the continuous surface and to cushion jolts as succeeding panels are moved from the upstream end of the conveyor and come into contact with the continuous line of panels passing beneath the flow head. Panels that are newly added to the upstream end of the line come into contact with the endmost panel in the line when the sealing strips are disposed beneath the flow head.