Abstract: A stator casing for air-cooled machines comprises a sheet metal jacket for mounting on the stator core and having a plurality of shaped-on, axially extending, radially projecting and peripherally spaced cooling ribs. The inner surface of sheet metal jacket is axially convex, the inside edge diameters at both ends of the sheet metal jacket preferably corresponding to the outside diameter of the associated stator core. At both ends, the sheet metal jacket also has reinforcements for preventing the enlargement of the edge diameter on pressing in the stator core. The arrangement is such that upon the pressing operation, the inner surface of the jacket portions of the stator casing located between the cooling ribs are mounted so uniformly and firmly on the stator core over the entire square dimensions thereof that at least from heat and force transfer standpoints, the stator casing and stator cores substantially form a constructional unit.