A method for applying a flexible annular strip to a radially inward oriented surface of a tire, the method comprising the steps of: providing a plurality of segments (20, 40) arranged about a central axis, each segment (20, 40) being movable between a collapsed radial position and an expanded radial position and having a radial outer surface for supporting at least a part of a length of the annular strip; providing a plurality of fingers arranged about the central axis and extending in a direction parallel to that axis, wherein each finger is movable between an inner radial position and an outer radial position, and wherein each angular area between two circumferentially neighboring segments (20, 40) is provided with at least one of the fingers; placing the annular strip about the radially outer surfaces of the segments (20, 40); placing excess lengths of the annular strip between two circumferentially neighboring segments (20, 40) about a radially inner surface of the finger provided in the angular area between these neighboring segments (20, 40); inserting the plurality of fingers and the plurality of segments (20, 40) supporting the annular strip into the tire's rim diameter with the central axis being positioned along the tire's axis; expanding each segment (20, 40) in an outer radial direction; and pressing the annular strip with the segments (20, 40) against the radially inward oriented surface of the tire, characterized in that each segment (20, 40) comprises at least one outwardly curved sheet for supporting the annular strip, wherein the curvature of the sheet is adapted to the circumferential curvature of the inward oriented surface of the tire. providing a plurality of segments (20, 40) arranged about a central axis, each segment (20, 40) being movable between a collapsed radial position and an expanded radial position and having a radial outer surface for supporting at least a part of a length of the annular strip; providing a plurality of fingers arranged about the central axis and extending in a direction parallel to that axis, wherein each finger is movable between an inner radial position and an outer radial position, and wherein each angular area between two circumferentially neighboring segments (20, 40) is provided with at least one of the fingers; placing the annular strip about the radially outer surfaces of the segments (20, 40); placing excess lengths of the annular strip between two circumferentially neighboring segments (20, 40) about a radially inner surface of the finger provided in the angular area between these neighboring segments (20, 40); inserting the plurality of fingers and the plurality of segments (20, 40) supporting the annular strip into the tire's rim diameter with the central axis being positioned along the tire's axis; expanding each segment (20, 40) in an outer radial direction; and pressing the annular strip with the segments (20, 40) against the radially inward oriented surface of the tire, characterized in that each segment (20, 40) comprises at least one outwardly curved sheet for supporting the annular strip, wherein the curvature of the sheet is adapted to the circumferential curvature of the inward oriented surface of the tire.