A catalytic combustion apparatus for gas turbine or an exhaust gas purifier apparatus comprises a honeycomb structure disposed in a flow tube. A ring-shaped fringe region of the lower-course end face of the honeycomb structure abuts against a ring-shaped second supporting member. The second supporting member has a plurality of passages which allow a fluid to flow out downstream from the fringe region. In this arrangement, the fluid from the fringe region is caused to flow downstream through these passages. Accordingly, tensile thermal stress is reduced, so that the honeycomb structure is prevented from being damaged thereby. Since the honeycomb structure is supported by the second supporting member in planar contact therewith, moreover, stress is prevented from being concentrated on part of the structure. Thus, the honeycomb structure can be securely supported without being damaged by any stress.