In the Netherlands, there is a large and widely used railway system that includes numerous railway bridges. This master thesis investigates the problems caused by these railway bridges. Since World War II, continu- ous welded rails have been used extensively throughout the Netherlands. These rails offer several advantages on embankments, such as reduced maintenance due to less vibration, increased passenger comfort, and reduced noise. However, continuous welded rails can cause problems when they run continuously over a bridge, as is the case in the Dutch railway system. Bridges are not continuous structures and have joints between the decks or between the deck and the transition structure. These joints allow the bridge deck to expand and contract due to temperature changes, move due to longitudinal forces from train braking and acceleration, and deflect due to the vertical load of the train, causing rotations at the ends of the bridge decks. This relative displacement between the bridge deck and the continuously welded rails creates addi- tional stresses in the rails. These additional stresses must not exceed the maximum allowable stress of the rail material, as this could cause the rails to buckle or fracture. Fixed points are often used in practice to limit the movement of the bridge deck and keep additional rail stresses within acceptable limits. This investiga- tion, however, focuses on understanding the interaction between the rails and the structure without the use of fixed points. The study assumes a railway bridge in the Netherlands with a ballast bed and uses concrete precast bridge decks. To gain initial knowledge of the problem and the various railway components and bridges, a literature review was conducted, and two existing railway bridge projects were analysed. It quickly became evident that there are two different bridge types relevant to the study of additional rail stresses: those without embankment influence and those with embankment influence. The study then identified parameters that could influence the magnitude of additional rail stresses to use them as variables in further investigations. Two longitudinal force models were created in SCIA Engineer: one without embankment influence (Model 1) and one with embankment influence (Model 2). These models are spring models where the stiffness of connections and elements is schematised as springs. The models were validated with hand calculations and used to obtain results for the influence of various parameters such as bridge deck span length, elastomeric bearings, bridge pier length, and foundation stiffness. The results of the two models were compared to understand the influence of the embankment. Additionally, the spring elongations of the non-linear springs between the bridge deck and the rails, representing the ballast bed, were examined to determine if they were in the linear or non-linear part of the spring characteristic to see if the springs slipped enforcing stress redis- tribution. Finally, the models assessed the individual contributions of three load cases (thermal, longitudinal traffic load, and vertical traffic load) to the combined additional rail stress. The results lead to the following conclusions: • When a structure is not influenced by the embankment, the magnitude of additional rail stresses depends on the stiffness of the substructure. The stiffness of the weakest component, in this case, the elastomeric bearings, has a significant influence. • When a structure is influenced by the embankment, the magnitude of additional rail stresses mainly depends on the dominant stiffness of the embankment, with the stiffness of the substructure having little to no influence. • Structures with embankment influence experience lower additional rail stresses due to the additional stiffness provided by the embankment. Problems with exceeding maximum permissible rail stresses occur mainly in relatively long railway bridge structures without embankment influence. • The vertical load has the largest contribution to the combined additional rail stresses for both structure types. • The thermal load has a larger influence on structures with embankment influence because these structures are more constrained by the embankment and thus more vulnerable to thermal deformations. • Linear summation of individual stress contributions from different load cases generally results in higher or equal stresses compared to non-linear combinations, making linear summation a conservative approach. The stress difference between linear summation and non-linear combination is usually only a few megapascals. If the springs between the bridge deck and the rails slip into the non-linear branch, this difference increases slightly but remains small. Based on these conclusions, the following recommendations can be made to prevent additional rail stresses from exceeding maximum permissible stresses without the use of fixed points and to streamline the process of longitudinal force analysis for engineers: • To prevent exceeding the maximum permissible stress in structures without embankment influence, consider using larger elastomeric bearings or less slender bridge decks that are less susceptible to deflection, thereby reducing additional rail stress, especially from vertical loads. • Since linear summation of individual contributions to additional rail stresses results in conservative and faster calculations, it is recommended to use linear calculations in the initial phase. Then, perform a final design review with non-linear calculations to ensure accuracy. This approach will significantly speed up the design process, as models will not need to run for hours or days each time.