In this paper, we examine the problem of determinining the electrostatic potential distribution and field intensity vector in the high voltage divider and around the power line support. The potential is defined as the solution of the Dirichlet problem for the Poisson equation, and the flow of the intensity vector is defined by integration of this vector along the contour located within the solution domain. The formulated problem is solved numerically by means of the finite volume method. This method representes some generalization of the finite difference method and allows discretization of differential equations on grids with arbitrary configuration. The idea of the method is to construct a basic grid, consisting of triangles, and the dual grid, consisting of the Voronoi cells. The differential equations are integrated over the volume of the Voronoi cell and then, using the divergence theorem, the volume integrals are replaced by surface integrals. The integrals over the cell surface are approximated by quadrature formulas. As a result, the original differential equation is replaced by a difference equation. This procedure is performed for all internal nodes, and therefore we obtain a system of linear algebraic equations. The technique was applied for solving two practically important problems. The fields of potential and of flow intensity vector have been constructed for the problem of determining the electrostatic field in the high-voltage divider. The divider capacity with the screen and without screen was determined. It was shown that the use of a cylindrical screen results in an almost twofold increase in capacity. The second considered problem is related to the calculation of the electrostatic field in the vicinity of the L-shaped support of the power line.