This chapter is devoted to a comparative analysis of methods of approximation by root-polynomial functions of ravine digital data, corresponded to boundary trajectories of short-focus electron beams. Till the recent time this problem solved only by complex numerical methods and the approximation task isn’t considered. Methods of approximation by the points and by the tangents are considered and analyzed in the paper. The advantages and disadvantages of both methods and possible areas of their practical application are indicated. Analytical relations for obtaining the coefficients of fifth and six order root-polynomial functions are also given. Both considered in chapter approximation methods has been tested on the original computer software created in Python. The chapter also presents and analyzes the corresponding results of testing the proposed approximation methods, describing of proposed numerical algorithms, and particularities of the developed computer software. As described result of the numerical testing it is proven, that the point approximation technique is simple and does not require large computational resources, but it is not always possible to achieve its convergence. The tangent approximation technique is more universal since it including in consideration the features of the set of approximated values, but at same time it is more complex and resource-intensive on the aspect of practical implementation at computer software. Level of approximation errors for both methods, using real experimental data, is similar, range of 10–15%.