Among all ship motions, the most critical one isthe roll motion for a submarine. The excessive roll motion can be harmful toboth ship's crew and equipment, especially in surfaced condition. For thisreason, it is important to predict the roll motion during the design stage toovercome excessive roll amplitudes. A mathematical model of the roll motion canbe used to predict the motion responses of a submarine. Estimation of the rolldamping is the most critical part to develop the mathematical model for abetter prediction of the roll motion. The roll damping can be obtainedexperimentally, numerically and empirically. Experimental methods are expensiveand time-consuming and empirical methods cannot be applied for all ship types.For this reason, numerical methods are frequently used due to the developmentof computer technologies in recent years, being economical and fast. In thisstudy, the mathematical model of roll decay motion for a submarine at surfacedcondition was obtained. The roll damping term was obtained numerically bycarrying out roll decay simulations using a commercial Computational FluidDynamic (CFD) code. The inertia and restoring terms were obtained empiricallyby using the submarine geometry. The mathematical model was obtained and theroll decay motion of the surfaced submarine was calculated with a 20 degreesinitial roll angle at zero speed and 5 kn, 7.5 kn and 10 kn forward speeds. Theresults were compared with numerical results and a good agreement was observed.