The article contains a comparative stability analysis of initial equilibrium forms of reticulated one-sheet hyperboloids of revolution.The calculations are performed taking into account the TAURINE geometric and the dual (geometric and material) nonlinearities.The influence of Drinks the shape of generatrix one-sheet hyperboloid of rotation on shells stability in these formulations of the problem is considered.The equilibrium curves of shells with load acting on the upper base are shown.