Floating offshore wind turbines are recently being considered widely for adoption in the wind power industry, attracting interest of several researchers and calling for the development of appropriate computational models and techniques. In the present work, a nonlinear finite-element formulation is proposed and applied to the static and dynamic analysis of mooring cables. Numerical examples are presented, and in particular, a mooring cable typically used for floating offshore wind turbines is analyzed. Hydrodynamic effects on the cable are accounted for using the Morison approach. A key enabling development here is an algorithmic tangent stiffness operator including hydrodynamic coupling. Numerical results also suggest that previous empirical hydrodynamic coefficients could be obtained by fully coupled fluid–structure interaction. Convergence-rate and energy-balance calculations have been used to demonstrate the accuracy of computed solutions. The introduction of the developed cable model in a framework for the study of the global behavior of floating offshore wind turbines is the subject of the current work. Source code developed for this work is available as online supplemental material with the paper