A steady prediction method is presented to compute dynamic damping coefficients for axisymmetric projectiles. Viscous flow analysis is essential to the steady method using a zero-spin coning motion in the inertial coordinate frame. The present method is applied to compute the pitching moment and the pitch-damping moment coefficients for the Army-Navy Spinning Rocket. The results are in good agreement with the parabolized Navier-Stokes data, range data, and unsteady prediction data. Predictions for Secant-Ogive-Cylinder configurations are performed to investigate effects of afterbody geometries. To investigate the geometrical effect and flow physics, the longitudinal developments of the coefficients are examined in detail.