Abstract The crack initiation stress (σ ci) and crack damage stress (σ cd) are two important stress thresholds for describing the progressive failure process of rocks. Accurately obtaining these two stress thresholds is crucial for analyzing the anisotropic characteristics of shale under the influence of bedding planes. The stress thresholds of rocks can be effectively obtained based on the response law of axial and circumferential strains during rock failure. Therefore, strain measurement methods have a significant impact on the stress threshold of rocks. Currently, there are mainly two methods to measure the axial strain of rock by displacement sensors, namely, axial extensometer and linear variable differential transformer (LVDT). To investigate the influence of strain measurement methods on σ ci and σ cd of shale, the stress thresholds and corresponding strain thresholds obtained by the extensometer and LVDT axial strain measurement methods were calculated based on the triaxial compression test results of Longmaxi shale under seven different bedding plane angles, and the differences in the calculation results based on the two methods were analysed. The discrete element method (DEM) was used to carry out numerical analysis, and the influence of the two measurement methods on the mechanical properties of rock was further studied. The research shows that the influence of strain measurement methods on the mechanical properties of shale is mainly reflected in deformation parameters, stress and strain thresholds and the post‒peak shape of the stress‒strain curve. For σ cd and its corresponding strain threshold, the calculation result of the extensometer is obviously smaller than that of the LVDT. In terms of σ cd, shale shows significant anisotropic characteristics.