In order to guarantee improved driving dynamics and comfort for railway passengers, it is common today to weld rails to a continuously track. However, viaducts constitute singularities in the railway substructure. Under thermal variations, creep, shrinkage, train passage and braking, the bridge structure deforms and leads to additional solicitation of the rail. The track-bridge interaction becomes a decisive criterion in railway bridge design. The forces in the rail must be limited in order to guarantee the safety of the traffic. The calculation model as well as the verification schema is regulated in the Eurocode EN 1991-2, chapter 6.5.4 and in Germany additionally in the Richtlinie 804. However, the backgrounds of the model assumptions and of the stress limits, which are necessary for the understanding of the calculations, are very poor documented. In the part 1 of this article, the history of the continuous welded rail and the development of the investigation of track-bridge interaction effects will be presented. Additionally, the model as well as the assumptions for the calculation will be presented. In the part 2, the backgrounds of the verification procedure and of its limits will be explained.