This study focuses on the need to detect tangential stress within steel components. A dual-channel electromagnetic ultrasonic transducer was developed, and a high-precision stress measurement system based on shear wave birefringence was established. The effects of different time-of-flight extraction methods in the time domain and various filtering algorithms in the frequency domain on stress measurement results were analyzed. Among these methods, the Butterworth filter demonstrated the best performance, improving the signal-to-noise ratio by 1.3 times compared to the original signal, with a standard deviation of 0.7 in repeated tests. For time-of-flight extraction, the autocorrelation method proved to be the most stable, with a standard deviation of only 0.2 in repeated tests. Stress measurements were conducted on two types of steel, Q345 and L360. Experimental results showed that the calibration curves for both materials achieved R2 values exceeding 0.98, and the absolute error in stress measurement was less than 10 MPa. The electromagnetic ultrasonic stress measurement system based on shear wave birefringence developed in this study exhibits high accuracy and stability.