An elastic limit state analysis of rigid jointed frames is presented on the basis of the non-linear stability theory. A simple two-bar frame, eccentrically loaded at its joint, and exhibiting both snap-through buckling and post-buckling strength, depending basically on the loading eccentricity, is used as model. It is found that: (a) in case of a post-buckling strength there is an elastic limit state (ultimate) load which-contrary to a limit point load, depends directly on the yield stress of the material of the frame and (b) at the critical eccentricity a sudden jump in the load-carrying capacity of the frame occurs. Moreover, the effects of several parameters on the non-linear and linear elastic limit state load, are assessed.