In　this　paper,　an　explicit　Green　function　in　terms　of　the　Stroh　eigenvalues　and　eigenvectors　for　generally　anisotropic　piezoelectric　materials　is　derived.　Based　on　this,　the　displacement　boundary　integral　equation　is　solved　numerically　by　a　collocation　method.　The　new　type　of　Green　function　for　3-D　anisotropic　piezoelectric　materials　is　successfully　incorporated　to　a　boundary　element　program.　By　using　the　developed　boundary　element　program,　the　mechanical　and　electric　variables　of　3-D　piezoelectric　cylinder　are　obtained　and　the　results　are　compared　with　the　corresponding　analytical　solutions　and　other　numerical　results　by　FEM.　These　results　are　agreed　very　well,　which　shows　the　precision　and　efficiency　of　the　present　method.　©　2016　IEEE.