The　mathematical　modelling　of　a　rotating　tapered　Timoshenko　beam　with　preset　and　pre-twist　angles　is　constructed.　The　partial　differential　equations　governing　the　six　degrees,　i.e.,　three　displacements　in　the　axial,　flapwise,　and　edgewise　directions　and　three　cross-sectional　angles　of　torsion,　flapwise　bending,　and　edgewise　bending,　are　obtained　by　the　Euler　angle　descriptions.　The　power　series　method　is　then　used　to　investigate　the　natural　frequencies　and　the　corresponding　complex　mode　functions.　It　is　found　that　all　the　natural　frequencies　are　increased　by　the　centrifugal　stiffening　except　the　twist　frequency,　which　is　slightly　decreased.　The　tapering　ratio　increases　the　first　transverse,　torsional,　and　axial　frequencies,　while　decreases　the　second　transverse　frequency.　Because　of　the　pre-twist,　all　the　directions　are　gyroscopically　coupled　with　the　phase　differences　among　the　six　degrees.