Single Point Mooring (SPM) Systems are in use worldwide as an FS, FPS or FPSO. The SPM System is of multi-component structure normally composed of a vessel, yoke or hawser, buoy and mooring chains. It is designed on the basis of model test results, because no suitable mathematical method is available for its motion and structural analysis under the combined loads condition. In this paper, we have derived a mathematical model of multi-component structure under the combined loads (wind, wave and current), considering higher order motions and hydro dynamic loads with Langley's constraint matrix. This time, we have applied same model above to SALM buoy and have compared its nu merical results with the same from model test. Following conclusions are obtained through comprehensive discussion (1) Constraint matrix of multi-body system is effective (2) SALM buoy system in small waves can be analyzed in frequency domain. (3) SALM buoy system in large waves should be analyzed in time domain considering higher order motions and hydro-dynamic loads.