This paper considers a case of punctual symmetry of a cyclic type and application of the R-functions method in building equations of symmetric objects of the boundaries. The R-functions method combined with the Ritz method for solving the Laplace equation in a complicated symmetric domain used. The problem of calculation of an electrostatic field in the system with crossed fields (cylindrical magnetron of reversed construction) is described. A wide frame of mathematical physics problems is connected with finding solutions for symmetric domains. Taking the symmetry into account in many cases results in a considerable simplification of both building of equations of a complex loci by R-functions method (RFM), and finding necessary solutions. Becomes possible to efficiently conduct calculations experiments in computer problems solved. The RFM, based on the R-functions theory, proposed by Rvachev V.L. in 1963 is essentially connected with building of loci equations [1]. However, the method of building of loci equations, possessing symmetry using RFM has been elaborated comparatively recently [2,3,4]. The solution of a boundary value problem is given for the Laplace equation in the domain having a complicated shape and possessing the punctual symmetry of a cyclic type.