It is a challenge for small, fixed-wing aerial vehicles to maintain flight stability under gusts. Inspired by the geometric features and the structural dynamic characteristics of the gliding bird wing, an elastic wing with similar characteristics was designed and optimised for use as part of unmanned aerial vehicle. A flight dynamic model, which includes the coupling of the longitudinal flight modes and the aeroelastic modes of the flexible wing, was built to analyse the mechanisms of specific coupling for the structural characteristics of the wing design, and how these specific couplings affect flight dynamics. The results showed that the bio-inspired elastic wing effectively allows alleviation of the gust response of the prototype through coupling effects of the short period and the first aeroelastic mode, even with a considerable frequency gap. These effects become more significant when the airspeed becomes larger. The conclusions of this research can facilitate further development of bird-sized unmanned aerial vehicles to extend their applications and make these vehicles more adaptive for flight in complex atmospheric environments.