This paper present the claculating method of optimum correction mass within permissible vibration linits for ratating machinery in two-plane field balancing. Basic technique of this method is based on influence coefficient method, and grphic vector composition that the resultant of two influence vectors obtained by trial mass have to be equilibrium with initial vibration vector in the each correction plane. Genetic algorithm which is a search algorithm based on the mechanism of natural selection and natural genetics is sued for vector composition, and SUMT method is used to objective function which seeks optimum correction mass for balancing a rotor.