This paper deals with a numerical model of top tension risers with hydropneumatic tensioner for Spar application in the Gulf of Mexico environment. The nonlinearity of the stiffness and the friction characteristics of the tensioner combined with stick-slip behavior of the riser keel joint are investigated. The relationship between tensions and strokes for the hydropneumatic tensioner is based on the ideal gas equation where the isotropic gas constant can be varied to achieve an optimum stroke design based on the tensioner stiffness. Challenges of modeling the coupling effects in the finite element (FE) method between the tensioner and hull motion are also presented. This new FE model is implemented into a fully-coupled time-domain coupled-dynamics-analysis program for floating bodies. The effect of nonlinearity of tensioner curve, tensioner friction, and riser keel friction is intensively investigated. The resultant global motion, TTR stroke, and tensions are systematically compared with those of a simple engineering approach, in which the nonlinear coupling effect is captured by linearization.