The development of technology implies the elaboration of new calculation methods. Such methods should be precise and efficient. The article presents a new method of railway track realignment. The example considered in the article consistsof an circular arc that is tangent to two straight lines. Authors show subsequent stages of realization of tasks of railway track realignment. Each formula is described in this paper. The novelty of this solution is use of the Nelder-Mead simplex method for

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... ing section of railway track geometry into set of measure points. The functional model of optimization problem was derived and discussed in details. The method of optimization problem was presented in the form of detailed algorithm.The example of use of proposed algorithm was presented and analysed.