Not only to relax and absorb thermal stress in the radial direction of a honeycomb body but also to sufficiently absorb thermal stress in the axial direction and to heighten adiabatic property to overcome problems of high cost and to improve durability.

A honeycomb body 1 is fitted in a casing 2 through elastic support bodies 3. The elastic support bodies 3 are installed at least in a waste gas inlet side end part of the honeycomb body 1 and either are joined to only one of the honeycomb body 1 and the casing 2 or are joined to neither of them. The elastic support bodies 3 are restrained in the axial direction by projections or the like which the casing 2 is worked from the outer surface to form. And a space between the honeycomb body 1 and the casing 2 is made to be of adiabatic structure. In this way, the device sufficiently keeps with the use environment stricter than the present situation.