This monograph provides a general background to the modeling of a special class of offshore structures known as compliant structures. External forcing is resisted by buoyancy and tension forces which become very large when the structure is slightly offset from its equilibrium. The technical development is presented in such a way as to demonstrate the generality of the modeling and to apply the techniques to the (i) articulated towers, (ii) tension leg platforms, and (iii) submerged pipes with internal flow. This book can be used as a supplementary graduate text book. Likely courses include those in advanced dynamics, ocean engineering, advanced vibration. The audience includes mechanical, civil, and marine engineers. Graduate students in engineering, faculty practitioners in industry and R&D organizations, and all those who have interest in dynamics, vibration, simulation, and offshore structures will find the book crucial.