Abstract: In order to reduce the deviation of online forecast for gap, an online calculation model of roll vertical stiffness called the fast calculation model of roll bounce was established on the base of the influence function method. This model does not need complicated experiment for compensation. Its calculation accuracy as well as calculation speed was improved. With the data from a 1580 hot tandem rolling system in Rizhao Rolling Mill, off-line calculations were done to analyze the influence of strip width on the roll vertical stiffness, and the results were compared with the ones by using traditional width compensation models. It takes 20 ms to calculate in every condition with the proposed model and the precision is improved, indicating that the model can be used online in a rolling mill.