Synthetic ropes are increasingly favored for use in offshore systems. Accurate predictions of the coupled hydrodynamic performance and structural response of offshore structures depends on a thorough understanding of the nonlinear characteristics of fiber materials. The objective of this study is to experimentally characterize the stiffness of a polyester mooring rope for a cylindrical floating production storage and offloading system. The quasi-static stiffness of the ropes and aged ropes after installation and the dynamic stiffness in various loading conditions were computed based on sub-rope tests following the guidelines from the American Bureau of Shipping. The quasi-static stiffness curves exhibited a linear decrease in values as the logarithm of the loading period (in minutes) increased. The dynamic stiffness was, in general, much higher than the quasi-static stiffness. The dynamic stiffness under various loading conditions revealed the complexities of the mechanical properties of polyester rope. Parameters such as the mean load, load amplitude, loading period, and loading cycles all had a notable impact. More tests are required to have a better understanding of their effects.