The　paper　presents　an　example　of　model　updating　of　both　the　mass　and　stiffness　parameters　of　a　curved　cable-stayed　bridge　in　Venice　(Italy).　Conventional　optimization　problems　of　mass　and　stiffness　using　ambient　vibration　data　are　prone　to　ill-posedness　and　ill-conditioning,　and　generally,　the　scholar　must　assume　one　of　the　two　to　achieve　a　reliable　estimate.　However,　it　is　possible　to　assess　the　mass　and　stiffness　from　ambient　vibration　tests　in　cable-stayed　bridges　following　a　two-step　procedure.　In　the　first　step,　the　scholar　can　assess　the　mass　matrix　from　the　cable　forces　estimated　from　the　natural　frequencies　of　the　cables.　Then,　the　unscaled　mode　shapes　and　natural　frequencies　are　used　to　tune　the　stiffness　matrix　in　a　second　step.　The　authors　proved　this　updating　approach　with　two　variance-based　sensitivity　analyses.　The　former　is　the　sensitivity　of　the　cable　forces　to　the　specific　mass　and　bearing　deformability.　The　latter　is　the　sensitivity　of　the　natural　frequencies　to　Young’s　moduli.　Two　global　optimization　algorithms　for　mutual　validation,　differential　evolution　(DE)　and　particle　swarm　optimization　(PSO),　are　then　implemented　for　the　model　calibration.　©　2023,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG.