This chapter covers the basic methods used in setting up a model of a typical railway vehicle and the types of analysis that can be carried out once the equations of motion have been produced. The historical development of the major simulation packages now used is also briefly covered. Typical analysis tasks such as modal analysis and running stability, simulation of ride on track with irregularities and analysis of curving behaviour are then covered in detail, with examples of typical applications. The main methods used for the assessment of the simulation results are also covered under each of these headings.