Uniaxial compressive strength is one of the basic parameters in the selection of building stones, which plays a significant role in their stability. Direct determination of this parameter in the laboratory involves problems such as preparing the test sample according to the standard, high cost of the test, and also its time-consuming nature. In order to overcome these problems, today, the development of indirect models in which uniaxial compressive strength is predicted based on other physical, mechanical, and textural properties of the stone has grown significantly. In this paper, by examining the relationship between the compression wave velocity (Vp) and the Schmidt hardness index (SHI) with uniaxial compressive strength, two empirical relations have been developed to estimate the compressive strength of carbonate building stones. The relations were constructed based on a database containing information on 63 samples of carbonate building stones (43 travertine samples and 20 marble samples) and using linear and nonlinear regression analyses in SPSS software, and their performance was evaluated. To evaluate the performance of the two relationships, statistical indices including coefficient of determination (R²), root mean square error (RMSE), and variance of error (VAF) were calculated for each relationship separately. Then, by examining and comparing the mentioned indices, it was determined that both linear and nonlinear relationships are reliable models for predicting the uniaxial compressive strength of carbonate building stones that can be used with acceptable accuracy.