In　this　paper　we　propose　a　gas-solid　free　boundary　problem　for　a　one-dimensional　model　system　of　a　compressible　viscous　gas　associated　with　the　inflow　problem,　where　the　solid　constantly　changes　into　the　gas　and　produces　the　inflow　of　the　gas　on　the　free　boundary.　We　first　show　the　existence　of　the　traveling　wave　solution　and　its　asymptotic　stability.　We　further　discuss　the　case　in　which　the　asymptotic　state　of　the　solution　is　given　by　a　combination　of　the　traveling　wave　solution　and　rarefaction　wave.