Abstract: A process for shaping glass sheets with a surface-shaping mould, against which the glass sheets are pressed using a pressure drop produced by sucking out the air from the space lying between the moulding face and that face of the glass sheet on the opposite side from the glass sheet, in which the pressure drop is a maximum at the edge of the glass sheet and decreases towards the center of the glass sheet, because of fact that air is introduced via air-inlet apertures opening into the moulding face, the air is again extracted by subjecting suction apertures made in the moulding face inside the region covered by the respective glass sheet to a vacuum. Furthermore, pressure between the glass sheet and the moulding face also in the region where the air is introduced is set to a value at most equal to the pressure beyond the glass sheet, in order to avoid any formation of bulging. A shaping mould suitable in particular for implementing this process is also described.