Classical rigid plastic optimum design cannot take into account displacement constraints or bounds on residual plastic strains which goal however maybe important when designing a structure. Using holonomic elastic-plastic constitutive law, the elastic-plastic optimum design problem can be formulated on the basis of the elastic-plastic analysis problem like the rigid plastic optimum design problem is based on rigid plastic limit analysis. In this way, the elastic properties can be included in the optimum design problem and also semi-rigid connections can be taken into account. This paper deals with several elasticplastic optimum design problems, namely, geometrically linear and nonlinear holonomic elastic-plastic optimum design and geometrically linear shakedown optimum design. Each of these problems leads to nonlinear programming. The different design problems are illustrated on a sample frame by using the MINOS mathematical programming package for the solution.Keywords holonomic elastic-plastic optimum design · geometrical nonlinearity · semi-rigid connection · shakedown optimum design · nonlinear programming AcknowledgementThe financial support of grant TÉT F-44/05 is gratefully acknowledged.