The requirement for wave-mode to determine stress intensityfactor (SIF) by ultrasonic wave is studied. The relationship between SIF and acoustic refractive index corresponding to longitudinal wave is used. The propagating velocities of both transverse and longitudinal waves in specimen and the refractive law are taken into account. It is found that, if a beam of ultrasonic longitudinal wave incidents upon the front surface of a loaded specimen with crack, two beams of ultrasonic longitudinal waves will pass through the rear surface of the specimen and four beams of them will pass through the front surface of the specimen since the reflection and the refraction. So, if ultrasonic wave is used to determine SIF, only the first one passing through the front (or rear) surface of the specimen can be used.