ComplexmodesandtravelingwavesinaxiallymovingTimoshenkobeamsarestudied.Duetotheaxiallymovingvelocity,complexmodesemergeinsteadofrealvaluemodes.Correspondingly,travelingwavesarepresentfortheaxiallymovingmaterialwhilestandingwavesdominateinthetraditionalstaticstructures.Theanalyticalresultsobtainedinthisstudyareverifiedwithanumericaldifferentialquadraturemethod.