Abstract: In an exhaust purifying device for an internal combustion engine, a honeycomb core is constituted by a single webbing which is implemented as foil of stainless steel. The webbing is made up of a flat portion and a corrugated portion adjoining each other in the longitudinal direction of the webbing. The flat portion is held by a core metal forming part of a jig at a particular position which is a predetermined distance remote from a position where the corrugated portion begins. The core metal is rotated about its own axis in such a direction that the flat portion underlies the corrugated portion. As the core metal is rotated, the flat portion forms a core portion around the core metal. Thereafter, the corrugated portion and flat portion are sequentially wound around the core metal while lying one above the other to thereby form the honeycomb core. The honeycomb core is received in a casing to be attached to the exhaust system of the engine.