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The article deals with the state-of-the-art in the field of Longitudinal critically refracted (L_CR) ultrasonic wave, for non-destructive material evaluation. It checks its capability for residual stress identification, and reviews positives and negatives related to its use. Obtained information within the article, are used for the understanding of essence of method and for the evaluation of its use in the practice. The paper is divided in few sections and sub-sections. In the first section, information about L_CR wave technique and factors correlated with this method, are provided. The next section writes about residual stresses and the importance of their identification. Next, the principal of residual stresses measurement and basic structure of measurement device, is described. A significant part of study, describes the state so far of theoretical and practical researches within the use of this method, in the technological practice of residual stress identification in surface layers of engineering components. In the conclusion, the obtained knowledges are summarised and evaluated. Related positive and negative aspects are included, with a verifying the need of future researches.