We　investigate　an　overdetermined　problem　for　the　torsion　equation　Delta　u　=　-1　in　an　unbounded　domain　in　R-3.　Under　some　additional　conditions,　we　show　that　the　solution　is　a　one-dimensional　quadratic　function　and　that　the　boundary　of　the　domain　is　a　pair　of　parallel　planes.　The　proof　is　based　on　the　maximum　principle.　(C)　2017　Elsevier　Inc.　All　rights　reserved.