In this paper we consider nematic liquid crystal (NLC) confined to cylindrical cavity under the homeotropic anchoring conditions. Saddles-splay and splay-bend terms influence on the axial director configuration stability in the presence magnetic field applied along the cavity axis is investigated. By using the Fourier expansion of director fluctuations azimuth angle our analytical method attack enables the stability conditions to be found in terms of the stability to each fluctuation mode. The dependence of the resultant stability threshold on the surfacelike elastic constant values is calculated. We have obtained the restrictions imposed on the constants to make possible the stabilization of the axial structure by the magnetic field.