Accurate evaluation of the mechanical response of railway tracks subjected to train-induced repeated loading is a prerequisite for their proper design and maintenance planning. A multitude of approaches have been developed over the years to accurately predict some of the most crucial aspects of track behaviour. This theme paper presents the recent advances in computational methods that can be employed to predict the performance of railway tracks and demonstrates their capabilities. Firstly, the suitability of the finite element (FE) method in understanding the soil arching mechanism, which governs the behaviour of the pile-supported railway embankments, is demonstrated. The influence of pile spacing on the soil arching mechanism is illustrated. Subsequently, the utilisation of the FE method in evaluating the performance of the ballasted and slab tracks is explored. The vertical stress variation and the accumulation of settlement in both tracks are compared. In addition, a novel computational approach based on a geotechnical rheological track model is presented that can be employed to predict the long-term performance of a standard section of the railway track as well as the critical zones, such as bridge-embankment transitions. Finally, the practical applications of the computational techniques and their future scope are discussed.