An externally-supported rotary fluid machinery and a method for eliminating axial rotor displacement. The fluid machinery includes a box body, an air cylinder and a rotor, wherein the rotor is eccentrically mounted in the air cylinder; the air cylinder is mounted in the box body; one end of a sliding plate is inserted in the rotor, and the other end is embedded in a wall of the air cylinder; a fluid inlet is provided on the box body, and a fluid outlet is provided on the air cylinder; a support end of the rotor protrudes out of the box body and is supported in a rotor bearing support structure; and a support end of the air cylinder also protrudes out of the box body and is supported in an air cylinder bearing support structure.