Some problems about elastic-plastic post-buckling

first parts of the paper deal with the analysis of simple models of elastic-plastic post-buckling. Attention is drawn to the specific effects, on the one hand, of the elastic-plastic nonlinearity, and on the other hand, of the geometrical non-linearity. Both analytical arguments and numerical computations are used, without any asymptotic assumptions. In the next part, the postbuckling of a compressed beam, chosen as an example closer to a real structure than the simple models, is computed by a finite element software. In each case, we get information about the global shape of the solution branches. As the main qualitative result of all these computations, we observe that the elastic-plastic behavior may lead to monotonous strictly increasing load/displacement curves. By comparison with the non monotonous curves usually deduced from asymptotic calculations, these results then stand for counter examples. Consequently, the paper aims at suggesting a special care when a postbuckling analysis is carried out in order to get maximal loads. The necessity of being careful is related to the kind and the number of problems that are presently open for an elastic-plastic bifurcation theory.