One or more sheets, e.g. two glass sheets heated to their deformation temperature are shaped by positioning the sheets on a sheet supporting surface of an outline mold. The outline mold and press face of a shaping member are moved relative to one another to bias the marginal edge portions of the upper sheet against the press face to establish an enclosure around the peripheral edges of the sheets. Vacuum is applied to the peripheral edges of the sheets to pull the air from between the sheets, and from between the press face and adjacent sheet surface as positive or atmospheric pressure is applied to bottom sheet to move the sheets against the press face. Optionally a vacuum can be pulled through passageways in the press face during the shaping of the sheets and pressurized air moved through the passageways after the sheets are shaped to move the sheets away from the press face.