A versatile and efficient method of analysis has been developed to analyze a mooring system composed of a floating structure, e.g., a ship, mooring lines, fenders, and an articulated tower. The floating structure is assumed to be large, but may have an arbitrary shape, and the tower is assumed to be axisymmetrical. Although the program treats the floating structure and tower as a system, each body may be examined alone in the absence of the other. The analysis is carried out in the time domain assuming rigid body motion, and the solution is generated by a forward integration scheme. This approach permits nonlinear line and fender forces to be incorporated readily into the analysis. The exciting forces in the analysis are wind, current, and waves, which are not necessarily collinear. The waves can be single frequency or composed of multiple frequency components. The vessel is free to respond to the exciting forces in six degrees of freedom—surge, heave, sway, roll, pitch, and yaw. The tower is free to respond in two degrees of freedom—oscillation and precession. The analysis has been extensively verified with several different model tests for different structure configurations in regular and random seas. These include an articulated tower, a single-point mooring tanker system, a floating caisson and an inclined mooring tower.