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Accurately determining rock elastic modulus (EM) and uniaxial compressive strength (UCS) using laboratory methods requires considerable time and cost. Hence, the development of models for estimating the mechanical properties of rock is a very attractive alternative. The current research was conducted to predict the UCS and EM of sandstone rocks using quartz%, feldspar%, fragments%, compressional wave velocity (PW), the Schmidt hardness number (SN), porosity, density, and water absorption via simple regression, multivariate regression (MVR), K-nearest neighbor (KNN), support vector regression (SVR) with a radial basis function, the adaptive neuro-fuzzy inference system (ANFIS) using the Gaussian membership (GM) function, and the back-propagation neural network (BPNN) based on various training algorithms. The samples were categorized as litharenite and feldspathic litharenite. By increasing the feldspar% and quartz% and decreasing the fragments%, the static properties increased. The results of the statistical analysis showed that the SN and porosity have the greatest effect on the UCS and EM, respectively. Among the Levenberg–Marquardt (LM), Bayesian regularization, and Scaled Conjugate Gradient training algorithms using the BPNN method, the LM achieved the best results in forecasting the UCS and EM. The ideal obtained BPNN, using a trial-and-error process, contains four neurons in a hidden layer with eight inputs. All five models attained acceptable accuracy (correlation coefficient greater than 70%) for estimating the static properties. By comparing the methods, the ANFIS showed higher precision than the other methods. The UCS and EM of the samples can be determined with very high accuracy (R2 > 99%). [ABSTRACT FROM AUTHOR]