As the floating offshore wind industry matures, it has become increasingly important for researchers to determine the next-generation materials and processes that will allow platforms to be deployed in intermediate (50–85 m) water depths, which challenge the efficiency of traditional catenary chain mooring systems and fixed-bottom jacket structures. One such technology, synthetic ropes, has in recent years come to the forefront of this effort. A significant challenge of designing synthetic rope moorings is capturing the complex physics of the materials, which exhibit viscoelastic and nonlinear elastic properties. Currently, numerical tools for modeling the dynamic behavior of floating offshore wind turbines (FOWTs) are limited to mooring materials that lack these strain rate-dependent properties and have a linear tension–strain response. In this article, a mooring modeling module, moordyn, which operates within the popular FOWT design and analysis program, openfast, was modified to allow for nonlinear elastic mooring materials to address one of these shortcomings in the numerical tools. Simulations from the modified openfast tool were then compared with 1:52-scale test data for a 6 MW FOWT semi-submersible platform in 55 m of water subjected to representative design load cases. A strong correlation between the simulations and test data was observed.