Consideration is given to the relationship between a stressed solid's state and the rate of ultrasonic wave propagation in the same solid. It has been found to what extent the above two quantities are correlated. An ultrasound technique is proposed for evaluating the level of stresses in solids. This was used for determining the state and rollability of billets for the production of thin-wall Zr-Nb alloy tubes, which are employed in nuclear industry for the fabrication of fuel element cladding.