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We present a workflow linking coupled fluid-flow and geomechanical simulation with seismic modelling to predict seismic anisotropy induced by non-hydrostatic stress changes. We generate seismic models from coupled simulations to examine the relationship between reservoir geometry, stress path and seismic anisotropy. The results indicate that geometry influences the evolution of stress, which leads to stress-induced seismic anisotropy. Although stress anisotropy is high for the small reservoir, the effect of stress arching and the ability of the side-burden to support the excess load limit the overall change in effective stress and hence seismic anisotropy. For the extensive reservoir, stress anisotropy and induced seismic anisotropy are high. The extensive and elongate reservoirs experience significant compaction, where the inefficiency of the developed stress arching in the side-burden cannot support the excess load. The elongate reservoir displays significant stress asymmetry, with seismic anisotropy developing predominantly along the long-edge of the reservoir. We show that the link between stress path parameters and seismic anisotropy is complex, where the anisotropic symmetry is controlled not only by model geometry but also the nonlinear rock physics model used. Nevertheless, a workflow has been developed to model seismic anisotropy induced by non-hydrostatic stress changes, allowing field observations of anisotropy to be linked with geomechanical models.