Self-centering　structures　have　become　the　focus　of　current　research　in　earthquake　engineering　due　to　their　excellent　re-centering　capability.　The　re-centering　capability　primarily　influences　the　residual　displacement　of　structures　that　is　an　essential　index　for　assessing　the　performance　of　post-earthquake　functional　and　withstand　subsequent　seismic　events　of　structures.　The　main　purpose　of　this　paper　is　to　investigate　the　re-centering　capability　of　partially　self-centering　structures　with　flag-shaped　hysteretic　behavior　subjected　to　near-fault　pulsed　ground　motion.　To　this　end,　the　current　provisions　on　residual　displacement　of　structures　were　first　introduced.　Then　two　self-centering　energy　dissipation　braces　(SCEBs)　with　fully　re-centering　capability　and　partially　centering　capability　are　developed,　and　their　hysteretic　behavior　are　investigated　by　quasi-static　cyclic　loading　tests.　To　capture　the　flag-shaped　hysteretic　behavior　of　such　self-centering　structures,　a　mathematical　restoring　force　model　based　on　the　Bouc-Wen　model　is　developed.　It　is　found　that　the　self-centering　capacity　of　a　partially　self-centering　structure　is　inversely　related　to　the　energy　dissipation　capacity,　resulting　in　a　reciprocal　effect　on　the　maximum　and　residual　deformations　of　the　structure　under　earthquakes.　The　influence　of　the　critical　parameters　(including　the　energy　dissipation　ratio　(beta),　the　post-yield　stiffness　ratio(alpha)　and　pulse　period　(Tp))　on　the　re-centering　capability　of　the　model　is　further　investigated　by　using　mathematical　and　statistical　methods.　Based　on　these　results,　the　design　recommended　values　of　beta　for　models　with　different　alpha　are　given,　furthermore,　a　simplified　calculation　formula　for　residual　displacement　of　partially　self-centering　structures　is　established　based　on　mathematical　statistics.