A block of electrically conductive material which is to be formed into a body with internal and/or external surfaces that approximate hyperboloids of one sheet is placed so that its axis is set at a predetermined skew angle with relation to a traveling EDM electrode wire. The electrode wire is then moved into cutting proximity of the body wire. Thereafter, by revolving the body about its own axis, the external and/or internal surfaces of the body will be cut into an approximate hyperbolic surface of revolution depending upon whether the body is positioned with the cutting wire outside of the body or in a previously formed longitudinal passage in the body. As an alternative technique, elongated channels can also be cut into the wall of the body by successively orienting the body to a selected number of angular positions, with the electrode wire being either outside of the body or in a previously formed passage in the body. At each of these angular positions, the electrode wire is moved orthogonally with respect to the axis of the wire, while both the body axis skew angle and the rotational position about that axis is controlled by cutting a channel or groove in the body to relieve stresses in the body material or to convey a coolant fluid.
