The field of the axially symmetrical systems is obtained in following sequence : the integral equation referring to the distribution of the magnetization’s vector in magnetic bodies is solved by the Galorkin’s method at first, and the field strength is obtained with use of found distribution of magnetization’s vector and primarily given distribution of current density at second. The analytical expressions for the computation of the scalar magnetic potential, magnetic strength of the current windings field and coefficients of the discretizated system of the integral equations are given. On purpose to reduce the multiplicity of the numerical integration they are expressed by complete elliptical integrals which are approximated with polynomials. The algorithm of computations is created by this method. The example, which illustrates the time needing for computations is given in this article.