Abstract: The unified strength theory was adopted as a yield criterion to describe an improving effect of intermediate principal stress on the coal seam strength for the determination of plastic zone in coal seam. Then,instability solutions such as the coal seam stress,the disturbance depth and the width of plastic zone were derived for preceding translatory coal seam bumps. Furthermore,the comparability analysis and verification of the proposed solution were compared with existing results available in the literature. Finally,parametric studies were carried out to investigate the intermediate principal stress effect,the depth and thickness of coal seam,and the strength parameters of coal seam. It is found here-in that the solutions proposed for the coal seam stress and the width of plastic zone are a set of orderly serialized re-sults,so they have wide theoretical value and good engineering applications. Meanwhile,the validity of the proposed solution is demonstrated by comparing it with the results from Mohr-Coulomb criterion,Hoek-Brown criterion and Lipp-mann’s theory. In addition,when the unified strength theory parameter b increases from 0 to 1,the damage range is decreased by 25. 3% ,and the expansion rate of plastic zone is decreased from 0. 63 to 0. 47. It means that the interme-diate principal stress has a significant impact on the translatory coal seam bump. Therefore,the intermediate principal stress effect should be reasonably considered to achieve more potentials of coal seam. Moreover,when the support force increases from 0 to 1 MPa,the width of plastic zone is averagely decreased by 21. 3% ,which indicates that the support needs to firmly and effectively be constructed to reduce damage ranges. Besides,a deep coal seam has poor stability and its damage range is large,while a thin coal seam is more prone to display small-scale bumps and instability. It is profound to account for the changes of coal seam strength parameters including cohesion and internal friction angle as important strength indexes,due to that their influences are very significant in excavation designs,especially for the in-ternal friction angle of coal seam.