This book treats the mechanical behavior of one-dimensional sandwich structures, a typicaloncept in the context of lightweight design. Such structures are composed of different constituent (e.g., layers) in order to achieve overall properties, which are better than for a single component alone. This book covers the basic mechanical load cases, i.e., tension/compression, bending, and shear. Based on this knowledge, different failure modes, i.e., plastic yielding, and global and local instabilities are investigated. In addition, an introduction to classic optimization problems, i.e., the formulation of an objective function (e.g., the weight of a structure) and corresponding restrictions, is included. The consideration here is limited to one- or two-dimensional design spaces, i.e., with a maximum of two design variables. For such simple cases, the minimum of the objective function can often be determined using analytical or graphical methods.