Stone is one of the most widely used and most common building materials which in the past has been used. Stones have a unique feature that are not comparable to other building materials. One of these features is the uniaxial compressive strength, which is one of the basic parameters in the selection of building stones which has a significant role in their stability. Therefore, the durability and resistance of rocks in different climatic conditions are very important. Climatic conditions in some cold regions of Iran and the occurrence of freeze cycles is one of the most important factors in weathering the rocks which affects the physical and mechanical properties of the rocks to some extent. To achieve this goal, it is necessary to be suggested the resistant and durable stone related to weather conditions. Direct measurement of uniaxial compressive strength after freeze-thaw cycles in the laboratory lead to problems such as sample preparation, cost of test and time-consuming. In order to overcome these problems, in this study, two models were developed to predict uniaxial compressive strength after freeze-thaw cycles (after 25 cycles) using p-wave velocity.Equations were developed based on a database containing information on 22 samples of carbonate building stones (12 types of travertine, 3 types of limestone and 7 types of marble) and using linear and nonlinear multivariate regression analyzes in software. To evaluate the performance of two equations, statistical indices including determination coefficient (R2), normalized mean square error (NRMSE) and variance account for (VAF) were calculated for each equation separately. Then, by comparing the mentioned statistical indices, it was found that the second model is higher ability of predicting uniaxial compressive strength after 25 cycles freeze-thaw compared to the first model. P-wave velocity is one of the most important parameters in geotechnical and rock mechanics projects and it is able to evaluate other non-destructive rock mechanical parameters. Due to the importance of this parameter, a nonlinear multivariate regression was developed to predict the p-wave velocity in each freeze and thaw cycle according to the rate of p-wave velocity changes during the freeze and thaw process. Then by considering and comparing the indices, it showed that the developed equation is a reliable model for predicting the p-wave velocity of carbonate building stone in each freeze and thaw cycle. In addition to the p-wave velocity and the uniaxial compressive strength, the long-term durability of carbonate building stone under freeze and thaw process has been investigated in this study. To investigate the long-term durability, two parameters of decay constant (?) and half-life index (??1/2), which were measured due to the decreasing p-wave velocity changes in the freeze and thaw process, were applied. Measuring decay constant (?) and half-life index (??1/2) is a difficult, tedious, time-consuming, and expensive process. Therefore, two regression models have been developed using statistical techniques CART regression tree to predict the decay constant and the half-life index of carbonate building stone with porosity. Comparison of the predicted values and the consideration of statistical indices showed that the two developed models tree are proper tools for predicting decay constant and half-life index