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The ultrasonic critically refracted longitudinal wave (Lcr wave) method is an effective tool for measuring surface stresses in a nondestructive way. Whether the stresses are uniaxial or biaxial, the result of the measurements depends on the ultrasonic time-of-flight difference and the stress coefficient. Besides these, the measuring direction is also a factor to be considered. However, this method can only be used to determine the stress parallel to the direction of wave propagation without considering the influence of the stress perpendicular to the direction of wave propagation. After carrying out a large number of experiments, it was found that the stress perpendicular to the direction of wave propagation has a significant effect on the results obtained. Meanwhile, in a biaxial stress state, the proportional relationship that is obtained between the variation in the stress of the specimens and the variation in the time of flight of Lcr waves is not valid. Instead, the proportional relationship between the variation in strain and the ultrasonic time-of-flight difference is established. Based on the acoustoelastic effect and generalized Hooke’s law, the concept of a strain coefficient is proposed. The longitudinal wave acoustoelastic equation under a biaxial stress state is derived for further study. This equation is applicable to calculating uniaxial and biaxial stresses and provides an effective method for measuring biaxial stress fields on the surfaces of materials.