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A New approach to the evaluation of the maximum and limit states of general inelastic structures subjected step loads is presented. The behavior of the elementary dynamic elastoplastic system with uni- axial or multi-axial slider is firstly studied. Full analytical solutions, given by the author, for the single-degree-of-freedom (SDOF) uniaxial elastoplastic system are then used to determine directly the maximum and limit states of the elementary dynamic multi-degree-of-freedom (MDOF) elastoplastic system taht has one multi-axial slider. This allows generalizing the direct method, which was proposed by Lee and Zarka and is applicable only to structures locally uniaxial, for general structures. Only two or three static elastoplastic analyses allow to obtain the residual stresses, plastic strains, and inelastic displacements of the maximum and limit states of the structures, resulting in a drastic saving in computation times and costs during inelastic dynamic analysis.