Random　properties　and　random　loads　are　highly　important　in　rotor　dynamic　analysis　because　they　cause　system　dynamic　responses　to　behave　randomly.　In　this　paper,　a　stochastical　finite　element　of　rotating　shaft　based　on　Timosheko　beam　theory　is　proposed　for　rotor　system　modeling,　in　which　material　and　geometric　random　properties　are　considered　one-dimensional　stochastic　field　functions.　A　random　response　analytical　method　is　developed　to　determine　the　statistics　of　the　dynamic　responses　of　stochastical　rotor　systems　under　random　loads.　The　numerically　obtained　whirl　speed　of　a　turbopump　rotor　system　is　compared　with　the　test　data　to　validate　the　proposed　model,　and　good　agreement　is　observed.　Linear　and　nonlinear　turbopump　rotor　systems　are　employed　to　compare　the　results　obtained　from　the　proposed　model　and　the　Monte　Carlo　simulation.　The　numerically　predicted　results,　which　coincide　well　with　Monte　Carlo　simulation　data,　demonstrate　the　feasibility　and　efficiency　of　the　proposed　stochastic　model　and　method　for　actual　rotor　system　analysis　and　design.