This paper theoretically investigates the localization of plastic buckling patterns in compression plates and cylindrical shells because this phenomenon has a large influence on the strength deterioration under cyclic loading. The localization behavior is caused by a plastic bifurcation on the decreasing equilibrium path subsequent to the maximum load point. Thus, we first show a rigorous numerical method based on the finite-element method technique to analyze the plastic bifurcation. Then, using this method, we examine the localization behavior of rectangular compression plate and that of the axisymmetric cylindrical shells under cyclic loading, Specifically, we investigate how the structural parameters and constitutive models affect the strength deterioration.