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The use of ultrasonic longitudinal critically refracted (LCR) waves is one approach used for near surface material characterization. It has been shown to be sensitive to stress and, in general, less sensitive to the effects of the texture of the material. Although the LCR wave is increasingly widely applied, in experiments the factors that influence the formation of the LCR beam are seldom discussed. This paper reports a new numerical model used to investigate the transducers' parameters that can contribute to the directionality of the L