The Niutitang Formation shale cores were observed by micro-slice observations and core X-ray whole-rock mineral diffraction analysis, and 7 groups of direct tensile numerical tests under different azimuth angles were performed. The test results showed that the calcite veins had a significant effect on the anisotropy of shale tensile strength. When the azimuth angle increased, the tensile strength gradually decreased. The bedding effect coefficient of tensile strength showed a curve-like growth trend with the increase of azimuth angle, which reached the maximum when α=90°, which was 0.127. The failure modes of shale samples at different angles were very complicated, which could be roughly divided into the following three categories: tree root shape (0°, 15°), step shape (30°, 45°, 60°) and river shape (75°, 90°). Fractures preferentially extended along calcite veins, which might inhibit the formation of complex fracture networks in the shale matrix during hydraulic fracturing. There were also significant differences in the release of dissipated energy under the calcite veins at different angles. The release of dissipated energy under the calcite veins at different angles was also significantly different. When α=0°, 15°, 30°, and 45°, the AE energy was small in the early stage, and increased rapidly to the maximum when it approached the peak stress. When α=60°, 75°, 90°, the AE energy was small in the early stage, and began to increase in the middle stage, and it was the largest when it was close to the peak stress. The cumulative AE energy increased roughly exponentially with increasing strain, and the growth process consisted of three stages: flat period, accelerated period and skyrocketing period. The research results had important reference value for the initiation of hydraulic fractures in shale reservoirs, the prediction of expansion, and the enhancement of oil recovery.