The nozzle made of flexible materials can expand and elongate its profile at different flight altitudes, greatly improving the engine’s endurance and ballistic accuracy. However, this also introduces the problem of structural vibration in the nozzle, which adversely affects engine performance. This paper introduces a high-precision hyperelastic material constitutive model for the flexible elongation nozzle and uses numerical simulation to conduct a detailed analysis of the internal pressure and structural vibration under aerodynamic pressure loads. As the flight altitude increases, the pressure magnitude and distribution on the inner wall of the same elongated flexible expansion section do not change. The pressure distribution on the inner wall of the flexible elongation expansion section exhibits certain nonlinear characteristics, and its magnitude decreases gradually along the axial position. The vibration of the elongated expansion nozzle profile becomes more intense with the increase in flight altitude. At high characteristic flight altitudes, the elongation length of the longer expansion section approaches an undamped vibration state.