This　paper　is　devoted　to　investigate　the　travelling　wave　motions　of　axially　moving　continua　with　time-varying,　harmonic　support,　boundary　conditions.　In　this　paper,　the　time-varying　support　is　assumed　to　vary　harmonically.　The　wave　motions　of　axially　moving　continua　with　different　supports　have　the　distinct　characteristics.　These　properties　are　not　only　related　to　the　positions　of　the　support,　but　also　to　the　direction　and　the　speed　of　the　transport　and　the　frequency　of　harmonic　support.　We　proceed　with　the　study　of　the　travelling　wave　motions　of　axially　moving　continua　with　the　support　changes　at　two　ends　and　between　them.　The　D＇Alembert＇s　method　and　the　modal　analysis　method　are　applied　to　axially　moving　string　and　beam,　respectively.　We　decompose　the　wave　motion　of　the　axially　moving　string　into　the　superposition　of　the　forward　travelling　wave　and　the　backward　travelling　wave.　With　the　increasing　of　the　transport　speed,　the　forward　travelling　wave　speed　increases,　the　natural　frequency　and　the　wavenumber　decrease.　However,　the　backward　travelling　wave　speed　decreases,　the　natural　frequency　and　the　wavenumber　increase.　No　matter　where　the　harmonic　support　is　set　at　the　output　end　or　the　incident　end,　the　string　model　always　exhibits　the　backward　travelling　wave　property.　But　a　certain　position　of　external　excitation　can　induce　resonance.　For　the　axially　moving　string,　the　travelling　wave　is　spotted　between　any　two　adjacent　nodes.　There　are　n　stationary　nodes　and　n+1　travelling　wave　intervals　when　the　frequency　of　harmonic　support　is　between　the　interval　of　the　nth　and　n+1th　natural　frequencies.　In　contrast　to　the　string　model,　there　are　only　n+1　travelling　wave　intervals　but　no　certain　stationary　nodes　under　the　aforesaid　frequency　with　respect　to　the　axially　moving　beam　©　Proceedings　of　the　26th　International　Congress　on　Sound　and　Vibration,　ICSV　2019.　All　rights　reserved.