Stress barriers play a key role in the propagation of hydraulic fractures. They are local maxima in the stress field that constrain vertical fracture propagation. The development of stress barriers is influenced by rock mechanical properties, pore pressure and tectonic stresses. However, stress prediction models are highly sensitive to available geophysical measurements and assumptions made on rock constitutive models. We compare stress estimations performed with elastic isotropic, anisotropic and viscoplastic models using Thomsen's notation (ɛ, δ, γ) to quantify anisotropy and its effects on hydraulic fracture geometry. Using a single depth for principal stress calibration, we compare stress distributions and simulate hydraulic fracture geometries along simple vertical and horizontal well sections. Prediction errors stemming from isotropic models along anisotropic intervals increase when tectonic stresses increase. Errors generated by either over- or underestimation of δ increase for tectonically passive environments, while errors generated by either over- or underestimation of ɛ increase for tectonically active environments. Additional corrections, but also uncertainties, can be introduced by considering viscoelastic rock behaviour. Because of stress shadowing and fracture interaction, the risk of stress barrier underestimation is higher when estimating hydraulic fracture geometries along the various stages of horizontal wells.