A process for foaming around a peripheral edge area of a cover (10) for a motor vehicle roof, the cover being placed on or in a foaming tool and the foam mass (18) being fed into the foaming tool such that two foam mass fronts are formed which run around the peripheral edge in the peripheral direction and merge with one another or meet one another in the merging area at a side opposite that at which the foam was introduced. The foaming tool is made such that, in the merging area, the cross section of the foam mass is reduced on the side opposite the ventilation side (40) of the foaming tool that is vented relative to the areas (42, 142) which border the merging area in order to prevent inclusion of gas bubbles in the merging area. Furthermore, a cover for a motor vehicle roof is produced which has a foamed peripheral edge area in which two foam mass fronts, which are formed during the peripheral foaming in a foaming tool, merge with one another. In the merging area, the cross section of the foam mass on the side opposite the ventilation side of the foaming tool is reduced relative to the areas which border the merging area.