In the previous paper the general formulation of curved rigid element models was described for the discrete limit analysis of several standard shells defined by the orthogonal curvilinear coordinates. These elements were derived without the approximation of shapes of curved surfaces. In this paper the triangular flat rigid element model is introduced for the analysis of shell structures of arbitrary shape. This type of element, being also used in the conventional finite element analysis, is of great use in the development of the general-purpose computer program, though it includes the shape approximation. The physical concept of the flat rigid element model can be obtained by the combined use of those of the plane strain and plate bending elements proposed by Kawai, and the development of the algorithm for the general thin shells was carried out recently by Toi. In this report the formulation is limited to the elasto-plastic analysis of static problems under the assumption of small deformation. The outline of the method of discrete limit analysis by using the flat rigid element model is described with some numerical examples on the standard problems. The application to the plastic instability and dynamic collapse problems is now under way and will be reported in the further reports.