This book provides a comprehensive yet concise presentation of the analysis methods of lightweight engineering in the context of the statics of beam structures and is divided into four sections. Starting from very general remarks on the fundamentals of elasticity theory, the first section also addresses plane problems as well as strength criteria of isotropic materials. The second section is devoted to the analytical treatment of the statics of beam structures, addressing beams under bending, shear and torsion. The third section deals with the work and energy methods in lightweight construction, spanning classical methods and modern computational methods such as the finite element method. Finally, the fourth section addresses more advanced beam models, discussing hybrid structures as well as laminated and sandwich beams, in addition to shear field beams and shear deformable beams. This book is intended for students at technical colleges and universities, as well as for engineers in practice and researchers in engineering.