An exhaust purifying device provided in an exhaust passage of an internal combustion engine comprises: a column-shaped honeycomb carrier; a cylindrical case member adapted to house the honeycomb carrier; a holding member provided between the honeycomb carrier and the case member to surround the outer circumference of the honeycomb carrier; buffer members provided on a peripheral edge of the edge surface of at least one side of an inflow side edge surface and an outflow side edge surface of the honeycomb carrier so as to regulate the movement of the honeycomb carrier in the central axis X direction; and setting members secured to the case member to regulate the movement of the buffer members by allowing their position regulation parts to contact the buffer members; wherein the buffer members are provided, on the outer circumferential sides, with recesses into which the position regulation parts of the setting members are fitted.