From　a　practical　point　of　view,　uncertainties　existing　in　structural　parameters　and　measurements　must　be　handled　in　order　to　provide　reliable　structural　condition　evaluations.　At　this　moment,　deterministic　model　updating　loses　its　practicability　and　a　stochastic　updating　procedure　should　be　employed　seeking　for　statistical　properties　of　parameters　and　responses.　Presently　this　topic　has　not　been　well　investigated　on　account　of　its　greater　complexity　in　theoretical　configuration　and　difficulty　in　inverse　problem　solutions　after　involving　uncertainty　analyses.　Due　to　it,　this　paper　attempts　to　develop　a　stochastic　model　updating　method　for　parameter　variability　estimation.　Uncertain　parameters　and　responses　are　correlated　through　stochastic　response　surface　models,　which　are　actually　explicit　polynomial　chaos　expansions　based　on　Hermite　polynomials.　Then　by　establishing　a　stochastic　inverse　problem,　parameter　means　and　standard　deviations　are　updated　in　a　separate　and　successive　way.　For　the　purposes　of　problem　simplification　and　optimization　efficiency,　in　each　updating　iteration　stochastic　response　surface　models　are　reconstructed　to　avoid　the　construction　and　analysis　of　sensitivity　matrices.　Meanwhile,　in　the　interest　of　investigating　the　effects　of　parameter　variability　on　responses,　a　parameter　sensitivity　analysis　method　has　been　developed　based　on　the　derivation　of　polynomial　chaos　expansions.　Lastly　the　feasibility　and　reliability　of　the　proposed　methods　have　been　validated　using　a　numerical　beam　and　then　a　set　of　nominally　identical　metal　plates.　After　comparing　with　a　perturbation　method,　it　is　found　that　the　proposed　method　can　estimate　parameter　variability　with　satisfactory　accuracy　and　the　complexity　of　the　inverse　problem　can　be　highly　reduced　resulting　in　cost-efficient　optimization.　©　2014　Elsevier　Ltd.