Drilling mud characteristics affect the stress distribution around the borehole, while anisotropic tensile strength determines the fracture behavior of the formation, but the combined effect of these factors is rarely considered in the prediction of fracture pressure. In this work, tensile strength anisotropy of shale rock was analyzed based on the Brazilian disc test (BDT), and the corresponding anisotropic tensile criteria were reviewed and contrasted with experimental results. The N-Z (Nova - Zaninetti) criterion is adopted to describe tensile strength anisotropy of shale rock. Based on the stress distribution model and the N-Z criterion, a model of shale rock fracture under the combined action of thermal and chemical factors was constructed. The solution of the model shows that chemical and thermal factors have a different effect on pore pressure distribution around the borehole. The effect of sedimentary layers, tensile strength anisotropy, in-situ stress and pore pressure on equivalent density of fracture pressure (EDFP) was also investigated. It is shown that the EDFP decreases with increasing dip angle at a given strike of the bedding plane and reaches a minimum value when the strike of the bedding plane is along the direction of the minimum horizontal stress. The decrease in EDFP caused by tensile strength anisotropy reaches or exceeds 10% of the value calculated for isotropic conditions. The more pronounced the anisotropy of strength, the smaller the possible value of EDFP. The higher the ratio of horizontal stresses and pore pressure, the more significant the effect of anisotropy on EDFP. It is also notable that increasing the temperature of the wellbore can improve EDFP parameters and enlarge the SMDW.