A mechanical non-contact gas seal including a rotary scaling ring and a stationary sealing ring that is engaged and held in an inner periphery of a seal case by means of O-rings so as to move in an axial direction thereof. The O-rings engage with the outer periphery of the stationary sealing ring and come in press contact with the inner periphery of the seal case to seal a gap between the stationary sealing ring and the seal case while allowing the stationary sealing ring to move in an axial direction. A resin coating of a thickness in the range of 5 to 100 μm is formed on the inner periphery of the seal case at least within a range in which the O-rings relatively move with the movement of the stationary sealing ring.