Soft biological tissues are exposed to moderately large stretches and they are prone to failure and fracture. Failure means the onset of damage and fracture means the damage localization into cracks with their subsequent propagation. There are various approaches to modeling failure and fracture and none of them is superior yet. The description of failure and fracture remains the main challenge in the general field of mechanics of materials for a century. Despite the enormous research effort the progress is mild. In this chapter, our recent work on the topic is briefly reviewed. Our approach is based on two physical assumptions, which avoid the introduction of internal variables. First, we assume that the number and energy of molecular bonds are bounded in a representative volume and, consequently, the macroscopic strain–energy function should also be bounded in the constitutive law. This notion leads to the introduction of energy limiters, which are calibrated in standard tests. Second, we assume that broken bonds are diffused during the fracture process. Such an assumption directly leads to a consideration of the coupled deformation–mass–sink problem. Mathematically, the coupling provides a regularized formulation for modeling crack propagation.