  We propose a robust approximate solver for the hydro-elastoplastic solid
material, a general constitutive law extensively applied in explosion and high
speed impact dynamics, and provide a natural transformation between the fluid
and solid in the case of phase transitions. The hydrostatic components of the
solid is described by a family of general Mie-Gr\"uneisen equation of state
(EOS), while the deviatoric component includes the elastic phase, linearly
hardened plastic phase and fluid phase. The approximate solver provides the
interface stress and normal velocity by an iterative method. The well-posedness
and convergence of our solver are proved with mild assumptions on the equations
of state. The proposed solver is applied in computing the numerical flux at the
phase interface for our compressible multi-medium flow simulation on Eulerian
girds. Several numerical examples, including Riemann problems, shock-bubble
interactions, implosions and high speed impact applications, are presented to
validate the approximate solver.
