A prediction method for dynamic damping coefficients using the unsteady Euler equations is presented. Direct unsteady simulation can be used to compote the pitch-damping moment without any geometric approximations when compared to the steady methods using the coning motions. A forced harmonic pitching motion is employed to generate the pitch-damping moments. To compute the pitch- and the roll-damping moments for the basic finner, a dual-time stepping algorithm combined with an implicit multigrid method is applied. The computed coefficients show good agreement with the experimental data. Grid refinement and parametric studies are performed to assess the accuracy of the numerical method. The linearity of the angular rates and the variation with Mach numbers are examined for both pitch- and roll-damping moment coefficients. Through analysis of the pressure distributions at various Mach numbers, the large variations of roll-damping moment coefficient in the transonic region are explained in detail.