Critically refracted longitudinal (Lcr) wave is the refraction of the longitudinal waves emitted from the first medium parallel with the surface of the second medium. The relationship between stress and wave velocity is expressed by acoustoelastic law. The theoretical relations for calculation of the acoustoelastic coefficient are so complex because of the need for measurement of material second and third-order elastic constants. The purpose of this research is the introduction of an accurate experimental method for acoustoelastic coefficient calculation, the effect of thickness of emission environment on the Lcr waves and, finally, the investigation of the stress measurement in shells and thin plates. By transmitting waves at the surface of the substance and investigating the waves received by the receiver transducers, the breakdown and the formation of different groups in the propagation of Lcr waves were detected. While the transmitted wave is composed of only one group. The results of this study show that longitudinal wave propagation in low thickness causes the formation of components of symmetrical and antisymmetric Lamb waves. By applying tensile stress on the sheet in which an Lcr wave was sent, it was determined that all groups received in the middle of the receiver transducer having a critical longitudinal nature behave identically to stress variations, while the Lamb's components behave differently to stress changes. Also, the study of variations of waves with stress less than yield point (up to 30MPa) shows that in a sample with a thickness of 0.5mm, the variations the flight time of the Lamb's S0 and A0 waves are 3.75 and 1.91 times the changes in the Lcr waves.