Critically refracted longitudinal (LCR) waves are commonly used to evaluate the residual stress of a material. The utilization of LCR waves is advantageous in that these waves are not sensitive to the texture of the material. Thus, LCR can be considered as a bulk longitudinal mode and can penetrate into the material well below its surface. However, while measuring the residual stress, the precision of the LCR wave travel-time is influenced by several uncertain factors. In order to further improve the accuracy of test results, we developed a measurement approach based on three aspects. First, the distances between the transmitter and the receivers were determined by transducer signal analysis. Second, for the residual stress detection to be consistent, transducers with different frequencies presented similar beam divergence angles. Finally, three different frequencies were used to evaluate the residual stress throughout the plate thickness. Based on the results of the above analysis, we used LCR waves to test 304 stainless steel plates. The detection error of residual stress measurement was ca. ±23 MPa. When compared with the X-ray diffraction approach, our method showed similar trends for the same regions of the specimens.