  The formation of singularity and breakdown of classical solutions to the
three-dimensional compressible viscoelasticity and inviscid elasticity are
considered. For the compressible inviscid elastic fluids, the finite-time
formation of singularity in classical solutions is proved for certain initial
data. For the compressible viscoelastic fluids, a criterion in term of the
temporal integral of the velocity gradient is obtained for the breakdown of
smooth solutions.
