Precision improvement in sheet metal stamping has been the concern that the stamping researchers have engaged in. In order to improve the forming precision of sheet metal in stamping, this paper devoted to establish the generalized holo-factors mathematical model of dimension-error and shape-error for sheet metal in stamping based on BP neural network. Factors influencing the forming precision of stamping sheet metal were divided, altogether ten factors, and the generalized holo-factors mathematical model of dimension-error and shape-error for sheet metal in stamping was established using the back-propagation algorithm of error based on BP neural network. The undetermined coefficients of the model previously established were soluble according to the simulation data of sheet punching combined with the specific shape based on the BP neural network. With this mathematical model, the forecast data compared with the validate data could be obtained, so as to verify the fine practicability that the previously established mathematical model had, and then, it was shown that the generalized holo-factors mathematical model of size error and shape-error had fine practicality and versatility. Based on the generalized holo-factors mathematical model of error exemplified by the cylindrical parts, a group of process parameters could be selected, in which forming thickness was between 0.713 mm and 1.335 mm, major strain was between 0.085 and 0.519, and minor strain was between −0.596 and 0.319 from the generalized holo-factors mathematical model prediction, at the same time, the forming thickness, the major strain, and the minor strain were in good condition.