The purpose of this monograph is to show how to model a compliant offshore structure in an ocean environment. Such structures are of increasing importance because of the desire to access the deep ocean. A brief history and an extensive review of the four existing transverse beam models are presented. The four beam models are Euler-Bernoulli, Rayleigh, shear and Timoshenko models. These are the fundamental models for the preliminary studies of offshore structures. The complete analytical solutions are given for each model. This review is followed by a chapter on the stochastic modelling of environmental forces. The waves are assumed to be random, and the fluid force is modelled using the Morison Equation. In subsequent chapters, the models are expanded to include the axial motion as well as the transverse motion in two and three dimensions. Numerical results are obtained using both deterministic and random forces. A detailed description of the numerical methods is provided so that the reader can adapt these methods to his or her particular problem. Researchers in the fields of structural mechanics and ocean engineering, especially those with an interest in nonlinear hybrid beam/cable models, will find this a useful book.