Biot's poroelasticity coupled with the thermal gradient has been extensively discussed in literature. In these articles, however, material anisotropy is ignored, and a homogenous-isotropic model is assumed. Elastic anisotropy plays a major role in the estimation of local stresses, especially in the perturbed region around the borehole. Moreover, the anisotropy in the thermic coefficients has considerable effects on pore pressure and effective stresses. Anisotropy has a greater effect on inclined boreholes, where the plane of elastic symmetry is unlikely to be aligned with the borehole axis. This work discusses the development of a numerical model using the finite element method for fully coupled anisotropic conductive-convective porothermoelasticity. The formulation is generalized such that it can be applied for inclined boreholes and incorporates true complete material anisotropy. Finally, a sensitivity analysis was undertaken to demonstrate how thermal stresses, thermo-osmosis and heat convection affect borehole stresses when elastic and thermic anisotropy are accounted for. The developed model can be applied to different facets of rock mechanics, geothermal, petroleum and drilling engineering applications. (C) 2016 Elsevier Ltd. All rights reserved.