Abstract: A new integration method proposed, i.e., the integral mean value theorem, is applied to simplifying the inner product of strain rate vector. The equivalent strain rate during barrel-shaped disk forging is expressed in terms of two-dimensional strain rate vector, then the strain rate ratio function and direction cosine of this vector are determined according to the integral mean value theorem, and its inner-product is integrated term by term. The integration results are summed up to obtain the formula of relevant barreling parameter b and analytical solution of the stress influence factor. A compression test was done to compare the values of the stress influence factor and total pressure thus calculated with those calculated according to Avitzur's approximate solution and the measured values given by the test. The comparison results show that the values thus calculated conform basically to Avitzur s upper bound approximation but are higher than measured ones, among which the relative error of pass reduction from 10% to 33% is 1.9%-9%.