Complex　modes　and　traveling　waves　in　axially　moving　Timoshenko　beams　are　studied.　Due　to　the　axially　moving　velocity,　complex　modes　emerge　instead　of　real　value　modes.　Correspondingly,　traveling　waves　are　present　for　the　axially　moving　material　while　standing　waves　dominate　in　the　traditional　static　structures.　The　analytical　results　obtained　in　this　study　are　verified　with　a　numerical　differential　quadrature　method.