Abstract: A new linear integration is proposed in this paper. First, effective strain rate for disk forging with bulge is expressed in terms of two-dimensional strain rate vector and its inner-product term by term integrated. Then, sum of the termwise integrated results is proved to be equal to that obtained from traditional immediate integration for plastic deformation power. Finally, an analytical solution of stress effective factor and corresponding calculation formula of bulge parameter b are deduced from velocity field for the disk forging. Furthermore, the actual press tests were performed and the stress factors calculated from above formula. The calculated results were compared with those obtained from Avitzur formula and total indicator reading of the machine. It turns out that the total pressures calculated are basically in agreement with those obtained from Avitzur's, and higher than the measured values. It still belongs to an upper bound solution.