<p>Flight stability is a critical aspect of the performance of fin-stabilized flying vehicles. The assessment of the stability criteria plays a crucial role in determining the overall success of a mission. Various factors such as body configuration, the center of gravity location, flight manoeuvres, and free-stream conditions all contribute to the flight stability of such vehicles. Free-stream conditions include various factors such as airspeed, angle of attack, and flight altitude. These parameters interact dynamically to determine the overall stability of the flying vehicle. This study examines the impact of free-stream conditions on the stability of a supersonic pitching fin-stabilized vehicle. Through numerical simulations, the study examines how variations in free-stream parameters including the airspeed and angle of attack affect static and dynamic stability of the flying vehicle. In addition, the impact of the pitch-damp characteristics is investigated at various frequency regimes ranging up to 200&#xa0;Hz. The validity of the results is confirmed as compared with wind tunnel data. Pitch-damp aerodynamic derivatives remain unchanged at various pitching frequencies but show significant variation with free-stream Mach number, indicating frequency-independent but airspeed-dependent behaviour. Overall, a complex interplay between pitching motion, airspeed, and stability characteristics in fin-stabilized vehicles is figured out. These insights provide valuable understanding regarding the correlation between the vehicle aerodynamic design and flight performance enhancement. Additionally, the pitch-damp derivative is assessed in terms of manoeuvrability and stability of the case study configuration. The study concludes with recommendations for further design requirements to enhance vehicle stability and performance.</p>