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This study describes the development and testing of a railway bridge weigh-in-motion (RB-WIM) system. The traditional bridge WIM (B-WIM) system developed for road bridges was extended here to calculate the weights of railway carriages. The system was tested using the measured response from a test bridge in Poland, and the accuracy of the system was assessed using statically-weighed trains. To accommodate variable velocity of the trains, the standard B-WIM algorithm, which assumes a constant velocity during the passage of a vehicle, was adjusted and the algorithm revised accordingly. The results showed that the vast majority of the calculated carriage weights fell within ±5% of their true, statically-weighed values. The sensitivity of the method to the calibration methods was then assessed using regression models, trained by different combinations of calibration trains.