The present article focuses on studying the experimental stress-strain behavior of eight different types of rocks tested under triaxial compressive loading conditions and thereafter assesses their behavior numerically using constitutive models for brittle materials like rock. First, the petrological, physical, and mechanical tests under no confinement are carried out for different types of rocks. Then, the rock specimens are tested under triaxial compressive loading conditions with varying confinement pressures following the International Society for Rock Mechanics and Rock Engineering (ISRM)-suggested method. The test results are then compiled to analyze the stress-strain responses and failure envelopes of different rocks at varying confining pressures using Mohr-Coulomb, Hoek-Brown, and Drucker-Prager failure criteria. Thereafter, a numerical model is developed in a commercially available finite element software package, ABAQUS, to validate the triaxial experimental test results. The numerical simulation is carried out for the triaxial compressive tests using the Mohr-Coulomb, Hoek-Brown, and Drucker-Prager constitutive models independently, and the stress-strain responses are compared with experimental results. It is concluded from the numerical study that the Mohr-Coulomb failure criterion shows a more conservative result than the Hoek-Brown and Drucker-Prager failure criteria.