Understanding the stress change in a reservoir generated by fluid production/injection is important for field development purposes. In this paper, we provide the Eshelby solution for stress and strain distribution inside and outside of an anisotropic poroelastic inhomogeneity due to pore pressure changes inside the inhomogeneity. The term anisotropic inhomogeneity refers to an inhomogeneity with anisotropic poroelastic constants. Some graphical results for strain and stress ratios for different material properties and geometries are presented as well. Anisotropy in elastic properties has been studied extensively in the last century; however, anisotropy in poroelastic properties, despite its potential significant impact in different engineering problems, has not been explored thoroughly. The results show how neglecting the effect of anisotropic poroelastic properties may result in large differences in calculated stresses. Due to the authors' primary interest in geomechanical problems, the discussions and examples are chosen for applications involving fluid withdrawal/injection into hydrocarbon reservoirs.