Three non-destructive testing techniques are developed and investigated to determine the Young’s modulus of elasticity of the trachea and the results are compared with the standard uniaxial state of stress method. These techniques are based on: (1) simulating the trachea as a pressurized vessel and deducing a special relationship between the pressure and the radial strain; (2) using two hydrophones and determining the variation in acoustic transmittance caused by the presence of the trachea in a propagation path within a water-bath; (3) considering the trachea as a thin cylindrical shell and determining the resonance radial vibration response. Discussion is presented to identify the “pros” and “cons” of each technique and final practical recommendations are made.