Based　on　the　linear　three-dimensional　piezoelasticity,　the　Legendre　orthogonal　polynomial　series　expansion　approach　is　used　for　determining　the　wave　characteristics　in　piezoelectric　hollow　cylinders　with　open　circuit.　Dispersion　curves　for　the　piezoelectric　and　the　corresponding　non-piezoelectric　hollow　cylinders　are　calculated　to　show　the　piezoelectric　effect.　The　differences　of　the　piezoelectric　effect　on　the　axially-symmetric　modes　and　flexural　modes　are　shown.　Electric　potential　distributions　are　used　to　show　the　piezoelectric　effect　on　flexural　torsional　modes.　Finally,　the　influences　of　the　ratio　of　radius　to　thickness　and　the　polarizing　direction　on　the　piezoelectric　effect　are　illustrated.