  We consider the free boundary problem of compressible isentropic neo-Hookean
viscoelastic fluid equations with surface tension. Under the physical kinetic
and dynamic conditions proposed on the free boundary, we investigate
regularities of classical solutions to viscoelastic fluid equations in Sobolev
spaces which are uniform in viscosity and justify the corresponding vanishing
viscosity limits. The key ingredient of our proof is that the deformation
gradient tensor in Lagrangian coordinates can be represented as a parameter in
terms of flow map so that the inherent structure of the elastic term improves
the uniform regularity of normal derivatives in the limit of vanishing
viscosity. This result indicates that the boundary layer does not appear in the
free boundary problem of compressible viscoelastic fluids which is different to
the case studied by the second author for the free boundary compressible
Navier-Stokes system.
