Abstract: A new criterion for optimum balancing of a flexible rotor is introduced,which is the minimum rotor strain energy criterion with constrains. This criterion meets the requirements for integral design of structure strength and performance of a gas turbine aeroengine. In this criterion the balance correction masses (quantity and orientation) are the optimum design variable, the objective function of optimization is the total strain energy of the rotor and its supports. The response amplitudes at several cross-section along the rotor are taken as its constraints. The Powell's method and the net random-ray method are chosen as optimum methods. A program is written with FORTRAN 77 for the whole optimization procedure. The program has been testified by a numerical example in comparison with its experiments.