Although　some　investigations　on　the　vibration　properties　of　multi-span　beams　have　been　conducted,　studies　on　multi-span　Timoshenko　beams　by　using　the　assumed　mode　method　have　been　relatively　few.　In　this　paper,　the　multi-span　Timoshenko　beams　are　investigated,　and　the　mode　shapes　of　the　beams　are　modified　by　the　interpolation　functions　to　model　the　vibration　modes　of　the　multi-span　beams.　Hamilton＇s　principle　is　applied　to　establish　the　equation　of　motion　of　the　structure,　and　the　natural　circular　frequencies　and　the　free　vibration　responses　of　the　multi-span　beams　are　obtained.　The　numerical　results　demonstrate　good　agreement　between　the　present　results　and　those　from　the　open　literature　and　the　ANSYS　software.　The　influences　of　the　length-thickness　ratio,　the　disorder　degree　and　the　span　number　on　the　free　vibration　of　the　structure　are　also　analyzed.　It　is　observed　that　the　displacement　amplitude　and　the　vibration　period　at　the　midpoint　of　the　three-span　Timoshenko　beams　are　reduced　when　the　disorder　degree　and　the　length-thickness　ratio　are　reduced.　The　increase　in　the　span　number　of　the　multi-span　beams　with　equal　spans　leads　to　the　decrease　in　the　displacement　amplitude　and　the　period　of　the　structures.　Furthermore,　some　interesting　phenomena　are　found,　e.g.,　the　same　even-order　frequencies　of　different　three-span　beams　are　equal　under　specific　disorder　degree.