Although　the　potential　of　shape　memory　alloys　(SMAs)　in　seismic　applications　has　been　well　recognized,　the　majority　of　the　past　research　was　directed　to　NiTi　SMAs.　This　study　aims　to　investigate　the　feasibility　of　using　a　novel　type　of　SMA,　termed　superelastic　monocrystalline　CuAlBe　SMA,　in　seismic　vibration　control.　According　to　prior　loading　tests,　CuAlBe　SMAs　had　an　excellent　superelasticity　behavior　with　the　largest　recoverable　strain　over　25%.　Within　the　superelastic　range,　CuAlBe　SMAs　shown　unloading　behavior　which　was　dependent　on　the　strain　amplitude　in　the　present　cycle,　which　could　not　be　captured　by　current　constitutive　models.　Hence,　a　new　constitutive　model　was　firstly　proposed　to　simulate　the　hysteretic　behavior　of　CuAlBe　SMAs,　and　a　good　agreement　is　found　between　the　experimental　data　and　numerical　simulations.　And　then,　to　explore　the　characteristics　and　advantages　in　terms　of　seismic　applications,　case　studies　on　single-degree-of-freedom　(SDOF)　systems　with　NiTi　and　CuAlBe　SMAs　were　carried　out.　Finally,　two　design　methods　were　used　to　size　the　NiTi　and　CuAlBe　SMAs,　and　the　corresponding　SDOF　systems　were　subjected　to　two　ensembles　of　earthquakes　associated　with　frequently　occurred　and　design　basis　seismic　hazard　levels.　The　simulation　results　indicated　that,　compared　with　NiTi　SMAs,　CuAlBe　SMAs　could　more　effectively　control　the　displacement　and　acceleration　demands,　if　their　ductility　capacity　was　fully　utilized　in　the　design　procedure.