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From core observations of shales of the Niutitang formation in the northern part of Guizhou Province, China, calcite was often found to act as a natural fracture filler and affect the extension of fractures in hydraulic fracturing. Therefore, it is crucial to understand the tensile mechanical behavior of shales by calcite veins. In this paper, by computed tomography scanning of shales containing calcite veins of different dip angles from the Niutitang formation, a three‐dimensional numerical model reflecting the internal fine structure of the shale was constructed. Direct tensile numerical simulations were carried out to investigate the effect of calcite veins at different angles on the fine‐scale damage process and mechanical properties of shale. The experimental results show that the tensile capacity of the shale increases with the increase in calcite veins. Depending on the dip angle of the calcite vein, the damage pattern of the shale is divided into three types of damage: pull‐off damage along the calcite vein, jagged damage, and horizontal damage perpendicular to the loading method. At high dip angles, the shale damage is more intense and the fracture network more complex. The temporal and spatial characteristics of the acoustic emissions provide a good indication of the microscopic behavior of the shale specimens during the damage process. The box dimension method was used to calculate the fractal dimension of the shale specimens at the final damage, and it was found that the damage was more intense and the fracture network was more complex at high dip angles, and there was an angular threshold. [ABSTRACT FROM AUTHOR]