An aeroelastic modeling capability of a flexible aircraft with gas turbine engines is developed using a computational fluid dynamics tool as an integration platform. The new modeling capability allows for the typical aeroelastic analysis to include a nonlinear dynamic model of the turbomachinery that is capable of capturing relevant gas dynamics. An example case of the aero-propulso-elastic (APE) modeling capability is explored for a supersonic transport vehicle with turbofan engines. An overview of the methodology for integrating the propulsion system and elastic vehicle is provided. This is followed by a study to explore coupling sensitivities compared against typical aeroelastic analysis. Dynamic and static vehicle responses are considered across key flight conditions and vehicle-level angles of attack, where the inclusion of the propulsion system has a 10% increase in vehicle wing tip deformations. It is found that the propulsion system is stable at various operating conditions, with structural oscillations having little impact on propulsion system performance. Perceived loudness, a key performance metric for a supersonic transport, is investigated using the APE model. Results lead to an approximately 4 dB increase in noise over a rigid body analysis that neglects the propulsion system. The greatest impacts are shown during off-nominal conditions.