The mooring system for a floating offshore wind turbine is a critical sub-system that ensures the safe station keeping of the platform and has a key influence on hydrodynamic stability. R&D efforts have increasingly explored the benefits of nonlinear mooring systems for this application, as they have the potential to reduce the peak mooring loads and fatigue cycling, ultimately reducing the system cost. This paper reports on a hydraulic based mooring component that possesses these characteristics, attributable mostly to the non-linear deformation of a flexible bladder. This is not a typical hydraulic component and, as a consequence, modeling its dynamic performance is non-trivial. This paper addresses this by introducing an analogy to numerically model the system, in which the functionality of the mooring component is compared to that of a hydraulic cylinder. The development of a working model in Simscape Fluids is outlined, and is subsequently used to simulate the IMS in a realistic environment. It is found that the numerical model captures a number of the dynamic performance characteristics observed in a previously tested prototype of the IMS.