In addition to its usefulness in modeling and simulation processes, the modulus of elasticity is an index which is highly used in biomedical identifications and tissue characterizations. For many composite and viscoelastic materials an "accurate modulus" is an idealistic hypothesis and an "equivalent modulus" is normally of a high biomechanical significance. The composite shape of the trachea, which consists of the smooth muscles and cartilage rings, renders the fact that an equivalent modulus is in place for many applications. In this paper three in-vitro nondestructive testing techniques are presented to determine the Young 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 studying the variation in acoustic transmittance caused by the presence of the trachea in a water-bath; (3) considering the trachea as a thin cylindrical shell and determining the resonance vibration response. Elaborate discussion is presented to identify the "pros" and "cons" of each technique and final practical recommendations are made.