The present study investigates the epicyclic pitching and yawing motion phenomenon of spinning symmetric projectiles applying the 6-DOF free flight dynamic simulation modelling for small-yaw flat-fire trajectories. The computational results are compared with the corresponding classical second order linear differential solution. The ammunition will be used is the .50 API M8 bullet tfiring from M2 machine gun launched horizontally from different firing angles on high-speed subsonic aircraft (helicopter). This analysis includes mean constant coefficients of the most significant aerodynamic forces, moments and Magnus effects, which have been taken from official tabulated database.