Rotating　shaft-disk-blade　(RSDB)　system　is　one　of　the　most　important　parts　of　turbomachinery,　such　as　aero-engine,　gas　turbine　and　power　plant.　The　coupling　vibration　of　RSDB　system　with　blade　crack　is　vital　for　the　blade　health　monitoring　and　crack　detection　of　rotating　blade.　This　study　aims　at　addressing　the　dynamic　modeling　and　steady-state　coupling　vibration　mechanism　of　RSDB　system　with　blade　crack.　First　and　foremost,　on　the　basis　of　the　stress　state　at　crack　section,　an　improved　analytical　breathing　crack　model　(modified　stress-based　breathing　crack　model,　MSBCM)　for　rotating　blade　is　proposed.　The　validity　of　the　proposed　breathing　crack　model　is　verified　by　comparing　the　results　obtained　by　MSBCM,　finite　element　contact　crack　model　and　conventional　analytical　crack　models.　The　comparative　results　suggest　that　MSBCM　is　of　high　fidelity　and　behaves　best　among　the　analytical　crack　models.　Subsequently,　a　comprehensive　dynamic　model　of　the　coupling　vibration　for　RSDB　system　with　blade　crack　is　formulated　on　the　basis　of　continuum　beam　theory　and　Lagrange　equation.　The　shaft　bending,　shaft　torsion,　blade　bending　and　blade　radial　deformation　are　comprehensively　considered　in　this　model.　The　validity　of　the　proposed　dynamic　model　is　verified　through　comparison　with　finite　element　simulation　and　experimentation　results.　By　introducing　the　proposed　MSBCM,　the　dynamic　coupling　vibration　model　of　the　RSDB　system　with　blade　crack　is　formulated.　At　last,　the　steady-state　coupling　vibration　mechanism　of　two　typical　structures　for　RSDB　system　is　comprehensively　investigated.　It　is　suggested　that　the　shaft　torsional　vibration　is　much　more　sensitive　to　blade　crack　than　the　shaft　bending　vibration　be,　which　indicates　that　the　vibration　features　of　shaft　torsional　vibration　may　offer　indicators　for　the　presence　of　blade　crack.