  We develop a framework in which to make sense of solutions containing the
vacuum in Lagrangian gas dynamics. At and near vacuum, the specific volume
becomes infinite and enclosed vacuums are represented by Dirac masses, so they
cannot be treated in the usual weak sense. However, the weak* solutions
recently introduced by the authors can be extended to include solutions
containing vacuums. We present a definition of these natural vacuum solutions
and provide explicit examples which demonstrate some of their features. Our
examples are isentropic for clarity, and we briefly discuss the extension to
the full $3\times3$ system of gas dynamics. We also extend our methods to
one-dimensional dynamic elasticity to show that fractures cannot form in an
entropy solution.
