Abstract: A rotary electrical machine, which is typically but not exclusively a motor vehicle alternator, is of the type comprising a casing consisting of two parts, each having a radial support surface, these support surfaces being opposed to each other with a stator lying between them. Between each end face of the stator and the corresponding support surface, there is at least one interposed elastic member which is in axial compression when the two casing parts are secured together. A set of elastic cushion blocks, spaced apart on a pitch circle defined by one of the casing parts, is interposed between the corresponding stator end face and a portion of the support surface of that casing part.