Optimal design of structures leads, as a rule, to slender and thin-walled shapes of the elements, and such elements are subject to the loss of stability. Hence the constraints of structural optimization usually include stability constraints, expressed by some eigenvalues. Optimal design under vibration constraints belongs also to optimization with respect to eigenvalues. The present volume gives a short introduction to structural optimization and then pays particular attention to multimodal optimization under stability and vibration constraints, both in elastic and inelastic range. One part is devoted to thin-walled bars optimized for interactive buckling with imperfections taken into account. The volume is of interest both to researchers and design engineers: it covers the most recent results of multimodal and interactive optimization, allowing for inelastic behaviour of structures, and the constraints discussed appear in almost all problems of engineering design.