A　practical　model　for　calculating　the　dynamic　characteristics　of　non-uniform　elastically　supported　beam　(bridge)　with　arbitrary　added　masses　is　given　according　to　the　structure　characteristics　of　non-uniform　beam　bridges.　The　improved　perturbation　method　(IPM)　is　obtained　by　modifying　the　mode　perturbation　method　based　on　Bernoulli-Euler　beam　theory.　In　the　modal　subspace　of　the　beam,　the　variable　coefficient　differential　vibration　equation　of　the　beam　with　arbitrary　added　masses　is　converted　to　nonlinear　algebraic　equations.　IPM　is　suitable　for　solving　the　vibration　equation　of　a　simply　supported　and　continuous　non-uniform　beam　(bridge).　The　examples　that　are　analyzed,　demonstrate　the　high　precision　and　fast　convergence　speed　of　the　IPM.　A　timesaving　method　(SIPM)　for　the　dynamic　characteristics　of　a　symmetrical　beam　(bridge)　based　on　the　symmetry　of　mode　shape　is　developed.　SIPM　has　about　half　the　number　of　coefficients　and　unknowns　as　does　IPM.　SIPM　has　higher　computational　efficiency　and　the　accuracy　of　SIPM　is　very　close　to　IPM.　Eventually,　the　effects　of　elastic　supports　and　added　masses　on　dynamic　characteristics　of　a　three-span　non-uniform　beam　bridge　are　reported.　©　2016,　Engineering　Mechanics　Press.　All　right　reserved.