This volume contains the contributions presented at the IUTAM Symposium on Variations of Domains and Free-Boundary Problems in Solid Mechanics, held in Paris, France, 22-25 April, 1997. In solid mechanics, free-boundary problems are relevant in a large variety of subjects such as optimization, optimal control, phase transition, metal casting, solidification and melting, stability analysis, inverse problems, propagating surface of discontinuity etc., and they raised interesting discussions in the past and recent literature.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 outstanding 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 originality of this book is that it is solid mechanics oriented, whereas other books published in the same field are mathematics oriented.