We obtain (3 + 1)- and (3 + 2)-dimensional global flat embeddings of 2 + 1
uncharged and charged black strings, respectively. In particular, the charg
ed black string, which is the dual solution of the Banados-Teitelboim-Zanel
li black holes, is shown to be embedded in the same global embedding Minkow
ski space structure as that of the 2 + 1 charged de Sitter black hole solut
ion.