The　propagation　behavior　of　horizontally　polarized　shear　waves　(SH-waves)　in　a　periodic　multilayered　piezoelectric　composite　structure　with　initial　stress　is　taken　into　account.　The　multilayered　piezoelectric　composite　structure　consists　of　piezoelectric　layer　bonded　perfectly　with　polymer　layer　alternately.　Solutions　of　the　mechanical　displacement　and　electrical　potential　function　are　obtained　by　solving　the　coupled　electromechanical　field　equations　for　the　piezoelectric　layer　and　the　polymeric　layer,　respectively.　The　phase　velocity　equation　of　the　SH-waves　in　the　periodic　multilayered　piezoelectric　structure　is　obtained　for　the　case　of　SH-waves　propagation　along　the　direction　normal　to　the　layering.　Influence　of　initial　stress　on　the　stop　band　effect　and　the　dispersion　relation　of　the　SH-waves　are　discussed　in　detail,　respectively.　One　set　of　piezoelectric　layer-polymeric　layer　combination　system　is　considered,　i.e.　PZP-5H　ceramic　layer-polythene　layer.　It　can　be　seen　from　our　research　results　that　the　stop　band　effect　of　the　SH-waves　propagation　is　dramatically　changed　with　the　increase　of　the　magnitude　of　the　absolute　value　of　initial　stress.　The　dispersion　relation　changes　remarkably　also,　as　the　magnitude　of　absolute　value　of　the　initial　stress　is　greater　than　100　MPa.　The　results　reported　in　our　research　work　can　be　used　as　the　benchmark　for　the　investigation　of　the　wave　propagation　in　the　piezoelectric　coupled　structures　and　are　theoretically　significant　in　the　design　of　wave　propagation　in　the　piezoelectric　coupled　structures　as　well.　(C)　2004　Elsevier　B.V.　All　rights　reserved.