A frame for an electric machine characterized by increased cooling capacity. An integral frame member has a pre-determined length defined by outer walls and inner walls, the inner walls defining a through void within which to accommodate stationary and rotating parts of the machine. A multitude of closely spaced-apart outer fins are integrally-formed with and project outwardly from the outer walls of the frame member for convection cooling of the frame by fluid contact iwth the enlarged surface areas of the fins. A multitude of closely spaced-apart inner fins are integrally-formed with and project inwardly from the inner walls of the frame member into the void defined thereby for convection cooling of the frame and the stationary and rotating parts of the machine within the frame by convection cooling by fluid contact with the enlarged surface area of the fins. The innermost ends of the fins are adapted to support thereon the stationary parts of the machine.