The present invention provides a stopper structure capable of preventing loosening of a shaft rod during use, and gas leakage which is likely to occur when the stopper structure is designed to allow gas to pass therethrough. The shaft rod 1 is adapted to be mounted in a mounting hole 2a of a refractory stopper 2, and formed to have an outer peripheral surface including a first tapered sub-surface 4a which increases in diameter toward an axially lower edge of the shaft rod. The mounting hole 2a of the refractory stopper 2 is formed to have an inner surface including a second tapered sub-surface 4b adapted to come into surface contact with the first tapered sub-surface 4a. The shaft rod 1 is adapted to be fastened to the refractory stopper so as to allow the first tapered sub-surface 4a to be brought into close surface contact with the second tapered sub-surface 4b. The distal end of the shaft rod 1 is formed in a configuration satisfying the following relation: tan θ≦D/2A, wherein: A is a length of the shaft rod 1 between a position of the shaft rod 1 corresponding to an upper edge surface 2S of the refractory stopper, and a start position of the first tapered sub-surface 4a; D is an outer diameter of the first tapered sub-surface 4a at the start position; and θ is a taper angle of the first tapered sub-surface 4a.