The wave motion equations of a tapered beam with respect to axial, torsional and flexural deformations are deduced including the transmission and waveguide equations. Combining the force equilibrium and displacement coordination conditions at the junction, we obtain the relation between the wavenumber and frequency, and the band gap properties of periodic tapered beam structures by the Bloch theorem. The modeling accuracy and efficiency of the traveling wave method are verified by the finite element method. The band gap properties of periodic tampered and uniform beam structures are analyzed and compared for the same materials and lengths as well as the same volumes.