In the previous paper the rigid flat plate element was derived for the discrete limit analysis of thin shell structures of arbitrary shape, and numerical results under the assumption of small deformations were shown on the standard elasto-plastic problems. In general the effect of geometrical nonlinearity such as large deformations and buckling behaviors is one of the main factors which determine the ultimate strength of thin-walled structures, however, the method for the general treatment of geometrical nonlinearity is not necessarily given in the conventional plastic analysis. In the present report the general computational algorithm for the discrete limit analysis of thin-walled plate and shell structures is presented, by using the flat rigid plate element of triangular shape. The present algorithm is characterized by the following statements : (1) The discrete analysis on the limit strength is possible for arbitrary thin-walled structural members, in which the effects of geometrical as well as material nonlinearities are taken into account. (2) In the application to the structural stability problems a family of simulation models with low degrees of freedom can be derived, including Shanley model in the plastic buckling problem of columns and Yoshimura buckle pattern observed in the non-axisymmetric buckling behavior of circular cylindrical shells, which can be effectively used in qualitative investigations on the instability phenomena of thin-walled structural members. (3) The formulation expressed in terms of stresses and strains is adopted instead of resultant forces, so that all kinds of constitutive equations can be easily introduced and the application to general material-nonlinear problems such as visco-elasto-plastic problems is possible.