A new shape of multisteady states current-potential curve is presented for the Volmer-Heyrovsky mechanism under Frumkin isotherm conditions. Linear stability of the steady states is studied for galvanostatic and potentiostatic regulation by drawing the pole and zero map of the electrode impedance. Non-linear stability is studied by calculating linear potential sweep voltammograms. The shapes of the voltammograms and those of steady state current-potential curves are the same as the shapes of the curves observed in the experimental study of the pitting of metals. Keywords: Bifurcation; Stability; Multisteady states; Volmer-Heyrovsky mechanism