The　band-gap　properties　of　non-uniform　periodic　beams　are　analyzed　using　numerical　and　experimental　methods.　The　flexural　wave　equations　are　established　based　on　the　Euler-Bernoulli　and　Timoshenko　beam　theories.　The　beams　with　periodically　variable　cross　sections　are　investigated.　The　transfer　matrix　method　is　used　to　explore　the　dynamic　behaviors　of　the　periodic　beams,　that　is,　the　natural　frequencies　of　the　finite　periodic　beams　with　different　cross-section　ratios　between　the　adjacent　sub-cells　and　the　band-gaps　of　the　infinite　periodic　beams　based　on　the　Bloch　theory.　The　validity　and　accuracy　of　the　band-gaps　acquired　by　the　present　method　are　verified　by　comparing　the　results　with　those　obtained　from　the　finite　element　method　and　the　vibration　experiments.　The　effects　of　the　different　lengths　of　adjacent　sub-cells　on　the　band-gap　properties　are　then　investigated.　The　research　results　and　conclusions　should　be　useful　in　the　study　of　vibration　control　applications.