A phenomenological energy-based model for stress-softening of isotropic, incompressible hyperelastic rubberlike materials is derived by using neo-Hookean material model. In this model, the microstructural damage is characterized by an exponential softening function that depends on the current magnitude of the strain–energy function and its maximum previous value in a deformation of the virgin material. This theoretical damage model is developed in order to provide a description of an idealized form of the Mullins effect for various deformation states. Non-dimensionalization of the problem allows easy comparison of the balloon shapes for different dynamic conditions on the same plot. Tension and stretch distribution along the balloon height can be predicted. Air drag is particularly useful in controlling the shape and size of the balloon. This book presents elastic behavior observed at large deformations where hyperelasticity can play a vital role in the dynamics of fracture, and that linear theory is incapable of fully capturing all fracture phenomena. It also helps in understanding the nonlinear behavior of hyperelastic material under various dynamic conditions.