Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This could result in a biased estimation of formation properties but could provide a means to estimate in situ stress from sonic logging data. To properly account for the formation property alteration, we propose an iterative numerical approach to calculate stress-induced anisotropy around a borehole by combining a rock physics model and a finite-element method. We tested the validity and accuracy of our approach by comparing numerical results to laboratory measurements of the stress-strain relation of a sample of Berea sandstone, which contains a borehole and is subjected to a uniaxial stress loading. Our iterative approach converges very fast and can be applied to calculate the spatially varying stiffness tensor of the formation around a borehole for any given stress state.