In producing a side-reinforced type runflat tire in which side reinforcing rubbers with generally crescent-shaped sections are interposed between a carcass and an inner liner, the first drums 11a, 11b on which the side-reinforcing rubbers are to be attached are so configured that their diameter do not substantially fluctuate along the axial direction. The expanding operation of the first drum, the mutually approaching operation of the first drums 11a, 11b and the approaching operation of the bead gripping rings 30A are synchronized. As a result, there is provided a tire and a method of its production capable of being produced by a multi-size mixed flow production system consisting of minimum equipments and of preventing air inclusions and wrinkles between the carcass member 4A and the side-reinforcing rubber 2A.