Synthetic ropes are increasingly being considered for various offshore and marine applications, including for mooring offshore wind turbines and for aquaculture cages. Studies have shown that nonlinear behaviors of a synthetic rope in a dynamic environment can complicate the mooring system analysis. Nonlinear stiffness coupled with time- and load history-dependent characteristics of fibrous materials can allow for over or under estimation of the mooring forces. It is critical that these nonlinear properties are incorporated correctly into a mooring model, especially for studies of structures’ performances in extreme events. The study aims at developing a simulation tool capable of predicting the dynamic behavior of highly extensible synthetic mooring system used in coastal and offshore floating structures. The program employs an implicit finite-difference approach to model the dynamic behaviors of the mooring line subjected to user-defined motions of the fairlead. As opposed to a linear stress-strain relationship typically incorporated in other mooring models, the current program is built with constitutive model of fibrous materials to account for the nonlinearity time- and load-dependent characteristics of synthetic lines. As part of the program, an inverted constitutive stress-strain model, in which stresses are calculated from given strains in stress-based formulas, were presented. Comparisons with published data indicates that the proposed inverted nonlinear stress-strain formulas were successfully integrated with the mooring solver. The coupled nonlinear mooring program predicts accurately both nonlinear reversible and irreversible deformations of synthetic cables.