Abstract: In order to improve the accuracy of the prediction of composite crack growth in linear elastic materials, and overcomes the defects that the commonly used maximal circumferential stress criterion does not consider material Poisson’s ratio and cannot distinguish plane stress and plane strain, starting from the strain point of view, and considering the role of T stress in brittle fracture, a linear elastic material crack propagation criterion based on the maximum tensile strain criterion was established and applied to study the influence of T stress and Poisson’s ratio on rock crack propagation. The results show that when the crack inclination angle β<45°, the prediction result of the crack initiation angle increases with the increase of α; when β>45°, the prediction result of the crack initiation angle decreases with the increase of α; The maximum circumferential strain criterion considering the T stress is more consistent with the experimental data, and the crack propagation is affected by the combined action of the T stress and the stress intensity factor. The combination of the strength factors, T stress and Poisson’s ratio have great influence on the fracture characteristics of rock cracks. The maximum circumferential strain criterion considering T stress, to judge the fracture characteristics of rock cracks, can make up for the insufficiency of the criterion of crack propagation based on stress.