The bifurcation of the axially symmetric equilibrium of shells of revolution with forming the hollows localized near the edge has been studied. The solving set of the first approximation equations with variable coefficients has been obtained. The analytical technique of building four solutions of this equation set has been proposed in the form of an exponential series. As an example the stability of a cylindrical shell under the eccentric compression has been considered. The critical values of the load parameters for this problem has been presented.