Shape　memory　alloys　(SMAs)　combine　super-elasticity　and　energy　dissipation　capacity　therefore　is　favored　in　seismic　hazard　mitigation.　Simplifications　are　necessary　to　incorporate　acquired　material　properties　through　material　testing　for　dynamic　analysis.　This　study　presents　a　methodology　to　integrate　SMA　material　testing,　model　inference,　and　probabilistic　seismic　analysis　for　uncertainty　quantification　of　SMA　model　uncertainty　on　SMA　based　structures.　The　proposed　methodology　is　applied　to　a　SMA-based　self-centering　concentrically　braced　frame　(SC-CBF).　The　posterior　distribution　of　SMA　modeling　parameters　is　first　obtained　through　the　MCMC　algorithm.　Considering　computational　cost　of　MCMC　algorithm,　linear　moments　method　is　introduced　to　sample　SMA　modeling　parameters.　Extensive　time-history　analysis　is　then　performed　to　quantify　the　effect　of　SMA　modelling　uncertainty　and　ground　motions　on　the　performance　of　SC-CBF.　Significant　response　changes　can　be　observed　in　SC-CBF　due　to　the　effect　of　uncertainty,　which　inevitably　affect　the　reliability　assessment　of　the　structure.　These　analysis　results　also　show　that　modeling　uncertainty　will　affect　seismic　performance　of　SMAbased　SC-CBF　but　its　influence　is　less　significant　than　that　caused　by　ground　motion　uncertainty　for　the　braced　frame　investigated　in　this　study.