PURPOSE: To prevent the generation of exhaust particulate embers in a filter for catching exhaust particulates, in regenerating the filter.

CONSTITUTION: A fine exhaust particle purifying device equipped with a honeycomb shaped filter 11 which is formed by alternately packing the exhaust gas inflow side and effluence side of the contiguous cells among a number of cells is installed in a casing, and is equipped with a heating means H at one edge part of the filter 11. In the first state, the inside of a packing member 15 in the vicinity of the outer peripheral part of the filter 11 among the packing member 14 at the filter end part on the remote side from the heating means H is made vacant. In the second state, the packing member 14 in the vicinity of the outer peripheral part of the filter among the packing members 14 at the filter end part on the remote side from the heating means H is set close to the heating means H side in comparison with the packing member 14 in the inner peripheral part of the filter. Accordingly, the fine exhaust particles in the filter 11 on the remote side from the heating means H are effectively prevented from being left in an uncombusted form in regeneration.