This paper investigates the mechanical behavior of soft elastomeric membranes under indentation by a rigid spherical object, with a particular focus on the failure mechanisms leading to puncture. The study examines both pristine membranes and those with pre-existing flaws, such as cracks, to explore how these imperfections affect the mechanical response and failure characteristics. An analytical axisymmetric model, based on a nonlinear solution for a hyperelastic, incompressible membrane, is presented. The prediction of the model are validated with experimental data obtained from indentation tests on silicone membranes. The study considers both stretch-based and energy-based criteria for fracture, providing insight into the conditions necessary for membrane failure and crack propagation.