Hydraulic fracturing of transverse isotropic reservoirs is of major interest for reservoir stimulation and in-situ stress estimation. Rock fabric anisotropy not only causes in-situ stress anisotropy, but also affects fracture initiation from the wellbore. In this study a semi-analytical method is used to investigate these effects with particular reference to shale stimulation. Using simplifying assumptions, equations are derived for stress distribution around the wellbore's walls. The model is then used to study the fracture initiation pressure variations with anisotropy. A sensitivity analysis is carried out on the impact of Young's modulus and Poisson's ration, on the fracture initiation pressure. The results are useful in designing hydraulic fractures and also can be used to develop information about in-situ rock properties using failure pressure values observed in the field. Finally, mechanical and permeability anisotropy are measured using Pulse Permeameter and triaxial tests on Pierre shale.