The rail straightening by means of roller straightening machines is in the focus of the present work. The straightening process is used to remove the undesirable rail bending caused by the uneven cooling from the rolling heat. However, by straightening an unfavourable residual stress state is introduced. For the measurement of this residual stress state a well known method from the literature is tested and further developed concerning the applicability to rails. The functionality of the extended method is confirmed by an alternative measurement. Theoretical considerations on bending in the straightening process lead to a new approach, where the curvature is identified as being the representative parameter for the straightening procedure. This consideration leads to the concept of curvature as an optimization strategy, which is a mathematical description of the curvature sequence. The strategy is tested on simplified models and is implemented on the rail in several stages using specific models. The material is characterized by cyclic tests as well as experiments close to the process and is described by an appropriate material model. The implementation of the straightening machine's bend sequence is done by a beam model with a user subroutine, which is necessary for finding the desired curvature and the correlated roller positions. Finally, a comprehensive model with submodelling technique calculates the residual stress state after straightening with the optimized straightening strategy. The verification of the models is based on on-site experiments under in-service conditions. The straightening model taking advantage of the curvature concept can be extended to arbitrary rail materials, as well as head-hardened rails.