PURPOSE: To enable to cool a multistage roots blower effectively, by sinking the multistage roots blower into water, and composing connecting portions between stages by means of communicating tubes working also as heat exchangers.

CONSTITUTION: A blower case body 6 has first'fifth vacuum chambers IWV, and respective vacuum chambers IWV are provided with inlet openings 1aW5a and discharge openings 1bW5b. The blower case body 6 is sunk in cooling water W, and respective vacuum chambers are connected together by inter-stage flexible pipes 22W25 which are disposed in the cooling water W and work as heat exchangers. Thereby, heat built up when gas which was sucked into the third vacuum chamber III via an inlet pipe 26 is compressed successively and discharged from a discharge tube 21 communicating with the fifth vacuum chamber V, is absorbed by the cooling water W, so that gas compression can be carried out effectively.