In a fluid machine such as multistage centrifugal compressor, the pressure of a working fluid is raised with the rotation of a impeller. A shaft sealing device is mounted at the end of the rotary shaft in order to prevent the working gas of the raised pressure from leaking out of the fluid machine and then polluting the surroundings. In a case where the fluid machine operates to rotate at high speed, a labyrinth sealing device is employed for the purpose of reducing a frictional loss in the shaft sealing device. The labyrinth sealing device includes a plurality of stages of labyrinth fins which are formed on a casing or the rotary shaft, and a layer of abradable coating to-be-bitten which is formed in the surface part of the rotary shaft or the casing opposing to the labyrinth fins. The clearances between the labyrinth fins and the rotary shaft or the casing are made narrower on the low-pressure side of the labyrinth sealing device than on the high-pressure side thereof. Thus, the fluid machine is run with the minimum clearance. Moreover, even when the coating layer has been lost in touch with the labyrinth fin or by peeling off, the labyrinth fin on the low-pressure side acts as a labyrinth seal.