The influence of axisymmetric localized imperfections of the middle surface (dents) on the stability of the axisymmetric membrane equilibrium of a thin shell of revolution is considered. Bifurcation to the nonaxisymmetric equilibrium form is researched. Under the assumption, that the loss of stability is localized in dent neighborhood, the asymptotic formulae for the critical load sensitivity to localized axisymmetric dents are obtained. The dependence of the imperfections sensitivity to the relation between shell curvature and initial membrane stresses is studied. Comparison of asymptotic and of the numerical results is carried out.