<p>The paper focuses on developing a new numerical program to determine the frequencies, modes, and the maximum amplitudes of vibration of traction, torsion, and bending modes of an axisymmetric supersonic nozzle by finite element method (FEM), using the inverse iteration algorithm, and the spectral shift. The goal is to eschew the resonance with the frequencies of the side loads caused in the not-adapted regime when varying the nozzle pressure ratio (NPR), and consequently avoid the rupture of the nozzle and the failure of the aerospace mission. We made the modelling of the nozzle geometry by thin walled circular and variable section of finite elements for free embedded beam, since the nozzle is considered as fixed at the throat and free at the exit section. The design is made by the method of characteristics (MOC) in the framework of high temperature (HT) model for air, to determine the contour of the nozzle, giving a uniform and parallel flow at the exit section. For the bending, the shear force and rotation effects are added in the two elementary matrices. We make the application for minimum length nozzle (MLN) given its current intensive aerospace application, and with best performances nozzle (BPN), and dual expansion nozzle (DEN), aiming to present an improvement for recently developed DEN. The results demonstrate an increase in the frequencies and decrease in the maximum amplitudes in the interest of the international aerospace community, up to 101% and 679% of DEN compared respectively to MLN and BPN when the exit Mach number <i>M</i>_E = 3.00, the stagnation temperature <i>T</i>₀ = 2000&#xa0;K and the throat radius nozzle ratio <i>λ</i> = 0.82. We made the validation for BPN central body, since it is of a constant cylindrical section, whose solution is in the literature for a traditional beam.</p>