The current works of revision of the Eurocodes (CEN250 project 2nd Eurocode generation), is an opportunity to update the simplified method (lambda factor method) for fatigue verification for road bridges. Especially as this method is based on old traffic models, it is necessary to establish an update consistent with current European road traffic. This thesis focuses on the max verification factor. The aim is to be able to determine new max curves using modern traffic models that are more reliable compared to current trends. In addition to this, an improvement is to be made to cover a larger number of cases, both in terms of influence lines and span lengths. The objective remains to propose new max curves taking into account the current European traffic observed in order to best monitor the behaviour of road bridges. Several types of traffic were used in order to have an overview and to be able to make a comparison between different models and especially WIM traffic measurements. In conclusion, a new proposal adapted for the verification method with lambdas factors is presented. This proposal takes into account the results of the different numerical simulations that could have been performed for a large variety of static systems and various traffic types.