  We study the free boundary problem for the flow of a compressible isentropic
inviscid elastic fluid. At the free boundary moving with the velocity of the
fluid particles the columns of the deformation gradient are tangent to the
boundary and the pressure vanishes outside the flow domain. We prove the
local-in-time existence of a unique smooth solution of the free boundary
problem provided that among three columns of the deformation gradient there are
two which are non-collinear vectors at each point of the initial free boundary.
If this non-collinearity condition fails, the local-in-time existence is proved
under the classical Rayleigh-Taylor sign condition satisfied at the first
moment. By constructing an Hadamard-type ill-posedness example for the frozen
coefficients linearized problem we show that the simultaneous failure of the
non-collinearity condition and the Rayleigh-Taylor sign condition leads to
Rayleigh-Taylor instability.
