The Kudo method for obtaining average pressures in some axisymmetric forming problems by the use of velocity fields having conical surfaces as discontinuity surfaces is reviewed in the paper. Following this it is shown that the extended treatment of admissible velocity fields is possible if the conical surfaces suggested by Kudo are replaced by curved surfaces. The application of these velocity fields to forming problems is then illustrated by simple examples of compression of cylindrical parts, and the improved upper bound to forming pressures is obtained.