In a method of fabricating an exhaust gas handling device, particularly an automotive emission control device, an insert, for example comprising a substrate and a support matting, is sensed as to its specific elasticity before it is clamped in place in an outer housing. For sensing, the insert is pressurized from without in a sensing station. Via the applied pressure and the displacement of the sensing tool the displacement of the insert at which it is to be clamped in place in the outer housing is determined. Then, the insert is fitted in an outer housing the inner dimensions of which correspond to the previously sensed wanted outer dimensions of the insert in the wanted compression.