Clinical interventions can change the mechanical environment of the tissues targeted for therapy. In order to design better procedures, it is important to understand cellular responses to altered mechanical stress. Rigid fixation is one example of a constraint imposed on living tissues as a result of implanted devices. This results in disturbed stress and strain fields, with potentially strong gradients. Herein, we numerically solve the governing nonlinear ordinary differential equation for the stress distribution in a finitely deformed anisotropic circular membrane with a concentric fixation by applying a zero-displacement condition at the inner circumference. Results show that rigid fixations yield distributions of stress and strain that are markedly different from tissue defects with traction-free boundaries. Moreover, the material anisotropy plays a significant role in the manner the stress redistributes regardless of the size of fixation. The present study will contribute to the design of experiments to determine cellular reactions involved in the failure of interventional treatments.