Owing　to　the　unique　superelasticity　and　satisfactory　energy　dissipation　capacity,　shape　memory　alloys　(SMAs)　show　great　potential　in　earthquake　engineering.　This　study　focused　on　establishing　analytical　method　and　finite　element　(FE)　model　for　the　buckling-restrained　SMA　(BRSMA)　based　self-centering　(SC)　dampers.　For　the　BRSMA-based　SC　damper,　the　lateral　deformation　of　the　slender　SMA　component　is　constrained　by　the　surrounding　buckling-restrained　plates　(BRPs).　Hence,　the　SMA　component　avoids　buckling　induced　instability　and　the　damper　accordingly　exhibits　stable　cyclic　behavior　under　tension-compression　loadings.　Although　the　compressive　behavior　has　been　obtained　through　cyclic　loading　tests,　an　in-depth　understanding　on　the　corresponding　force-displacement　relationship　is　required.　As　such,　a　simple　analytical　method　was　proposed　for　estimating　the　compressive　strength　capacity　of　the　BRSMA-based　SC　damper.　Besides,　the　FE　model　was　built　to　provide　additional　information　that　was　difficult　to　obtain　in　physical　model　tests.　The　accuracy　of　the　analytical　method　and　FE　model　was　confirmed　by　the　testing　results.　The　verified　FE　model　was　further　used　to　conduct　the　parametric　analysis.　The　parameters　of　interest　included　the　shape　of　the　reduced　section,　the　dimension　of　the　BRSMA　components,　the　gap　between　the　BRSMA　components　and　BRPs　and　the　number　of　bolts.　The　findings　of　this　paper　not　only　promote　understanding　on　the　cyclic　behavior　of　this　new　damper,　but　also　provide　suggestions　and　guidelines　for　future　design.