Purpose. Determination of improvement ways of admissible speeds of train movement on the difficult sections of а railroad plan. Methodology. Mathematical modeling of the train traffic is used to achieve the purpose of research. The average weighted speed and elevation of outer rail is predicted on this basis. Findings. The case analysis of the speeds determination in curved sections of track was carried out. The above mentioned track sections adversely affect the ride comfort and the intensity of the way disorder, as well as the reasons that contribute to the speed limits traffic on the railways of Ukraine. The technique of performing the calculations for determining the permissible train speeds was developed and tested on real curves of railways, were the accelerated movement of trains was introduced. Proposals on automate calculations in distances and services by way of determining the permissible speeds in curves were developed. Originality. Methodology of determining the permissible motion speeds and elevation of outer rails on the difficult sections of the railway plan was developed. This approach allows you to get a rational decisions on reorganization of plan based on local conditions. Practical value. The developed technique of definition of admissible speeds of motion in curves was implemented as a program DopShvid. The program was tested on real railway sections, where the accelerated train motion was introduced.