in the shaping of sheets of heat - softenable material such as glass and other deformable materials , a hot sheet engages an apertured lower sheet of a deformable vacuum box while the sheet and the box are flat and conforms to the changing shape of the box . since the box intermittently engages a hot deformable sheet for shaping and releases the deformed sheet after shaping , its lower apertured sheet is exposed to a wide temperature cycle , which causes the lower apertured sheet to warp away from the shape desired for the deformable sheet . the present invention provides structure for the deformable box that avoids such warpage while retaining the ability of the box to maintain sufficient vacuum to hold and distort the hot sheet while the box changes shape into its desired configuration with minimum warpage therefrom so that the hot sheet develops a desired curved configuration while held thereagainst during deformation of the box .