This paper applies a model reduction method for linear parameter-varying (LPV) sys- tems based on parameter-varying balanced realization techniques to a body freedom flutter (BFF) vehicle. The BFF vehicle has a coupled short period and first bending mode with additional structural bending and torsion modes that couple with the rigid body dynamics. These models describe the BFF vehicle dynamics with considerable accuracy, but result in high-order state space models which make controller design extremely difficult. Hence, re- duced order models for control synthesis are generated by retaining a common set of states across the flight envelope. Initially the full order BFF models of 148 states are reduced to 43 states using standard truncation and residualisation techniques. The application of balanced realization techniques at individual point designs result in 20 state models. Unfortunately, the application of balanced realization techniques at individual operating conditions results in different states being eliminated at each operating condition. The objective of LPV model reduction is to further reduce the model state order across the flight envelope while retaining consistent states in the LPV model. The resulting reduced order LPV models with 26 states capture the dynamics of interest and can be used in the synthesis of active flutter suppression controllers.