An apparatus for laminating a layer of polymer plastic film--such as non-oriented polyurethane or polyvinyl butyral laminated with oriented polyethylene teraphthalate--to glass, is taught. A saddle is provided having essentially the same contour as the glass that contacts it during the lamination process; and at least the surface of the saddle has an essentially identical coefficient of heat expansion and contraction as the glass, so that there is no significant slippage of the glass with respect to the saddle as the glass and polymer plastic film are heated and cooled. A segmented saddle may be provided having segments with substantially different coefficient of heat expansion and contraction than that of glass, but by being spatially isolated there is no gross expansion or contraction of the saddle face compared with that of the glass. A compression ram presses against the polymer film to be laminated to the glass. Either or both of the saddle and the ram is heated, usually the saddle. The ram may have a flexible hard face and an extendible piston which operates against it to ensure initial contact of the ram and film to the glass at the center of the glass; and as the ram continues to press against the film, the extendible piston is withdrawn for complete area contact. Methods of operating the apparatus are taught; and the invention contemplates multi-laminar glass/plastic structures.