This collection of papers on solid mechanics explores free-boundary problems which are involved in a large variety of methods such as optimization, optimal control, phase transition, metal casting, solidification and melting, stability analysis and inverse problems. Although the physics behind these phenomena is immense, the mathematical analyses often present many common features. The three aspects - mechanical modelling, mathematical formulation and numerical resolution - are the main points of this book. It gives a review of the state of the art in free-boundary problems for research engineers and researchers in applied mechanics and applied mathematics. The focus of the book is solid mechanics oriented.