Since direct tensile testing is time-consuming and expensive, the Brazilian test may overestimate the tensile strength of rocks because of its biaxial stress instead of the uniaxial tension condition, an alternative testing method is required to determine tensile strength of intact rock samples. The aim of this paper is to introduce a new push–pull tensile testing apparatus (PPTA), which can be used for determining direct tensile strength of cylindrical intact rock specimens. The PPTA introduces a new clamping mechanism that can also be utilized for the determination of conventional direct tensile strength of intact rock specimens. During the study, direct tensile tests and indirect Brazilian tests were carried out using rock specimens and artificial rock specimens that were made by using graded river sand, cement, and water mixtures to compare results obtained from the PPTA tests. Results of the experimental study have shown that there is a good correlation between the results obtained from the direct tensile tests and the PPTA. In addition, elastic and elasto-plastic numerical modeling studies were also carried out using the three-dimensional finite difference method (FLAC 3-D) to investigate stress development within rock sample during testing and failure initiation. Results of the modeling studies showed that failure of the core sample is due to maximum principal tensile stresses and crack initiation starts from the outer periphery of the core and propagates inside the center, which is an acceptable failure mode for direct tensile testing. Finally, results of the experimental and numerical studies have shown that push-pull tensile testing apparatus (PPTA) is a practical and reliable tool for determining direct tensile strength of intact rocks. Because it does not require sample preparation, it can easily be used either in laboratory or in situ.