The study of deformation in membranes has implications in the field of medicine, mechanobiology, and mechanics. In this study, we consider the case of a thin hyperelastic, incompressible, isotropic membrane with a central hole subjected to outer boundary stretching. The membrane is assumed to follow a quadratic Mooney-Rivlin constitutive relation. Using principles of mechanics and equilibrium equations, the system was formulated, and the resulting boundary value problem is solved using a modified shooting method based on the regula-falsi method. The model is examined numerically for various outer stretches, material parameters, and hole sizes.