The　wave　differential　equation　of　prestressed　box　beam　with　any　cross-section　was　deduced.　For　the　purpose　of　calculating　transmission　and　reflection　coefficient　matrix　in　segment　with　gradually　varying　cross　section　of　the　prestressed　beam,　the　segment　was　divided　into　several　pieces　of　beam　with　constant　section.　The　transmission　and　reflection　coefficient　matrix　of　the　wave　amplitudes　at　the　big　end　and　the　little　end　of　the　segment　with　non-uniform　cross-section　was　calculated　based　on　the　transfer　matrix　method　in　wave　analysis　on　sandwich　structure,　and　the　matrix　accuracy　which　is　affected　by　the　division　number　and　cross-section　dimension　in　the　beam　segment　was　analyzed　by　performing　several　subroutines　programmed　based　on　Maple　software.　The　accuracy　of　the　calculation　was　verified　by　using　the　solution　of　wave　differential　equation　according　to　the　Galerkin　method,　in　which　the　combination　of　first　kind　Bessel　functions　was　employed　as　trial　functions.　What　is　worth　to　be　mentioned　is　that　the　trial　functions　used　in　the　paper　can　be　used　generally　and　accurately　to　obtain　the　approximate　solutions　of　differential　equation　of　higher　order　which　contain　coefficients　of　series　functions　with　higher-order　terms.