This article presents the results of studies of limestone samples from the Sary-Tash deposit. The samples were subjected to various types of influences, such as mechanical cyclic fatigue tests, thermal cycling tests when heated to 600°C, and thermal tests during freezing/thawing. Relationships between the acoustic quality factor (Q-factor) and strength were obtained for different types of tests. For mechanical fatigue tests and thermal tests when freezing/thawing, similar dependences of the Q-factor and strength were obtained, which are approximated by logarithmic dependencies σm = 0.25 .ln Q + 1.04 for mechanical testing, and σf= 0.23 .ln Q + 1.07 for thermal testing by freezing/thawing. For thermal testing when heated up to 600°C, the form of the relationship between the acoustic Q-factor and strength has a more complicated character. The estimation of the possibility of substituting one type of test with the other was carried out by checking the statistical hypotheses about the equality of the regression dependencies' coefficients. The calculations showed that the differences in the coefficients a₀ and a₁ for mechanical and thermal tests during freezing/thawing were insignificant. This fact confirms the possibility using data interchangeably, and of reducing the duration and cost of tests.