A flange sealing system includes two bodies that each have a respective flat surface and are interconnected so that the surfaces face one another. At least one of the bodies has a groove with parallel side walls recessed into the flat surface. An elastic profile with an H-shaped cross-section is arranged in the groove in such a way that at least a part of the vertical regions of the elastic profile is arranged parallel to the side walls of the groove. In at least one portion of the space between the vertical regions of the elastic profile, a cured liquid is arranged in such a way that the profile is adhesively connected to the groove in the region of the base surface of the groove. The cured liquid is elastic.