Rocks underground often have pores and bedding planes, which are appropriate to be described by the transversely isotropic poroelastic constitutive model. Drilling boreholes in these rocks must be careful, since stresses and pore pressure would change with time, because of the inherent time dependent property of poroelasticity as well as pore fluid diffusion. In order to correlate the behavior of transversely isotropic poroelastic model of borehole in plane strain with the behavior of isotropic poroelastic model, an equivalent isotropic material is built with carefully chosen material constants, and correlation rules are successfully developed. With the solutions for the borehole problem in an isotropic model obtained previously, the solutions to transversely isotropic model can be obtained. Two cases of tensile failure and six cases of shear failure for the borehole are considered. As a result, the allowable borehole working pressure range is formulated by explicit expressions. The failure case, time, and location could also be obtained for any given drilling pressure. Results obtained from the Hooke’s traditional elastic model are compared, and it is found that poroelastic model is necessary in borehole safety check, while Hooke’s model is not on the safe side.