A method for producing a tubular catalytic converter, which includes a monolith wrapped in a mat and is disposed in a housing, includes forming a stepped longitudinal fold on a longitudinal side of a housing blank, wherein the longitudinal side on both sides of the fold to be formed is clamped by electrodes of opposite polarity across the fold. Electrode pairs on one side of the fold to be formed are then offset with respect to electrodes on the other side of the fold and the electrodes of opposite polarity move closer together, while a current is flowing between the electrodes of opposite polarity, heating the material in the fold. Opposing longitudinal sides of the tubular housing are then materially joined along the stepped longitudinal fold with the overlap to produce the housing for the tubular catalytic converter.