Abstract: To study the exterior ballistic characteristics of suspended acoustic countermeasure devices, a six-degree-of-freedom spatial motion mathematical model is established based on principles of kinematics and dynamics. The quaternion method is introduced to improve the mathematical model, enabling comprehensive exterior ballistic simulation including vertical trajectories. The simulation program is used to simulate the exterior ballistic of suspended acoustic countermeasure devices launched in the transverse direction of underwater vehicles. The effects of underwater vehicle speed, muzzle speed, distance between device's center of gravity and center of buoyancy on the exterior ballistic are compared and analyzed. The results indicate that to enhance exterior ballistic safety, the platform speed should be appropriately reduced, the muzzle velocity should be increased, and the distance between device's center of gravity and center of buoyancy should not be excessively large.