We present an overview of a variational approach to modelling fracture initiation in the framework of nonlinear elasticity. The underlying principle is that energy minimizing deformations of an elastic body may develop singularities when the body is subjected to large boundary displacements or loads. These singularities often bear a striking resemblance to fracture mechanisms observed in polymers. Experiments indicate that voids may form in polymer samples (that appear macroscopically perfect) when the samples are subjected to large tensile stresses. This phenomenon of cavitation can be viewed as the growth of infinitesimal pre-existing holes in the material or as the spontaneous creation of new holes in an initially perfect body. In this talk we adopt both viewpoints simultaneously. Mathematically, this is achieved by the use of deformations whose point singularities are constrained to be at certain fixed points (the "flaws" in the material). We show that, under suitable hypotheses, the energetically optimal location for a single flaw can be computed from a singular solution to a related problem from linear elasticity. One intriguing consequence of the above approach is that cavitation may occur at a point which is not energetically optimal. We show that such a disparity will produce configurational forces (of a type previously identified in the context of defects in crystals) and conjecture that this may provide a mathematical explanation for crack initiation. Much of the above work is joint with S.J. Spector (S. Illinois University).