This article relates to optimization and assessment of railway polynomial transition curves. The search for the optimum shape meant here the evaluation of the transition curve properties based on chosen dynamical quantity and generation of such a curve shape. In the study, 2-axle rail vehicle was used. The rail model represented 2-axle freight car of the average values of parameters. Mathematically understood optimization methods were also applied. As the transition curve, the authors used polynomials of 9th and 11th degrees. As the criterion of the assessment, the integral of change of lateral acceleration along the route was also used. Wide range of the circular arc radii was applied by the authors. The mentioned radii were: 600 m, 900 m, 1200 m, 2000 m and 3000 m. In the work the results of the optimization – types of the curvatures of the optimum transition curves, as well as the vehicle dynamics were presented.