In　this　article,　we　present　a　new　numerical　method　for　solving　the　steady　Oseen　equations　in　an　unbounded　plane　domain.　The　technique　consists　in　coupling　the　boundary　integral　and　the　finite　element　methods.　An　artificial　smooth　boundary　is　introduced　separating　an　interior　inhomogeneous　region　from　an　exterior　homogeneous　one.　The　solution　in　exterior　region　is　represented　by　an　integral　equation　over　the　artificial　boundary.　This　integral　equation　is　incorporated　into　a　velocity-pressure　formulation　for　the　interior　region,　and　a　finite　element　method　is　used　to　approximate　the　resulting　variational　problem;　Finally,　the　optimal　error　estimates　of　the　numerical　solution　are　derived.　Computer　results　will　be　discussed　in　a　forthcoming　paper.　(C)　1999　Elsevier　Science　Ltd.　All　rights　reserved.