  We consider the problem of dynamic cavity formation in isotropic compressible
nonlinear elastic media. For the equations of radial elasticity we construct
self-similar weak solutions that describe a cavity emanating from a state of
uniform deformation. For dimensions $d =2, 3$ we show that cavity formation is
necessarily associated with a unique precursor shock. We also study the
bifurcation diagram and do a detailed analysis of the singular asymptotics
associated to cavity initiation as a function of the cavity speed of the
self-similar profiles. We show that for stress free cavities the critical
stretching associated with dynamically cavitating solutions coincides with the
critical stretching in the bifurcation diagram of equilibrium elasticity. Our
analysis treats both stress-free cavities and cavities with contents.
