The geological conditions in deep formations are very complex, especially in bedding strata. Nowadays, with increase in drilling depth, the instability of the borehole caused by the failure of weak planes will seriously affect the drilling progress. In this paper, the physical and mechanical properties of rocks with weak planes are summarized and analyzed, and the applicability of strength anisotropy models are discussed. Considering the permeability anisotropy and heat transfer anisotropy of the rocks with weak planes, the specific borehole stability theory is further developed for the surrounding rock with weak planes. It is found that some strength anisotropic models may lose their applicability under certain circumstances; furthermore, neglect of the anisotropic characteristics of the permeability and heat transfer of the weak-plane rocks in the deep strata in the high temperature environment may lead to big errors in the calculation of stresses, failure area and collapse pressure of the borehole.