Provided is a rotary electric machine housing and a rotary electric machine equipped with the same. The housing allows the reduction of press fitting force required in each of two press fitting steps and has a high cooling effect. This rotary electric machine housing includes an internal cylinder 10 allowing press fitting of a stator 20 along an inner diameter end of the internal cylinder. The internal cylinder 10 has an internal cylinder-side tapered face on its outer diameter end surface. The housing further includes an external cylinder 11 having an external cylinder-side tapered face on an inner diameter end of the external cylinder. The external cylinder-side tapered face fits onto the internal cylinder-side tapered face. It is preferred that an inner diameter of the internal cylinder be smaller than an outer diameter of the stator; an outer diameter of the internal cylinder be larger than an inner diameter of the external cylinder; and a difference between the outer diameter of the internal cylinder and the inner diameter of the external cylinder be larger than a difference between the inner diameter of the internal cylinder and the outer diameter of the stator.