It　is　practically　difficult　to　collect　sufficient　probability　information　for　structural　random　variables.　Moreover,　actual　dynamic　loads　also　increase　the　difficulty　in　probability-based　reliability　evaluation.　Therefore,　dynamic　loads　are　first　simplified　into　quasi-static　loads.　Then　a　new　concept　of　quasi-static　deflection　surface　has　been　proposed　based　on　the　concepts　of　quasi-static　deflection　curves　and　displacement　influence　lines　commonly-used　in　the　civil　engineering　realm.　The　mathematical　expressions　of　deflection　surfaces　are　then　deduced　using　the　principle　of　virtual　work.　Uncertainties　in　the　geometrical　dimensions,　material　properties　and　external　loads　of　a　structure　are　reflected　by　interval　variables,　by　which　means　a　quasi-static　deflection　surface　is　extended　to　a　quasi-static　deflection　interval　enveloping　surface.　After　that,　an　experimental　simply　supported　steel　box　beam　has　been　taken　as　an　example　for　validation.　A　quasi-static　interval　reliability　index　is　proposed　according　to　the　relationship　between　the　measured　deflection　surface　of　the　beam　and　its　deflection　interval　enveloping　surface.　The　reliability　of　the　beam　before　and　after　damage　can　be　evaluated　using　the　interval　reliability　index.　The　analysis　results　demonstrate　that　the　uncertainties　in　both　structural　parameters　and　loads　can　be　effectively　considered　in　the　quasi-static　deflection　interval　enveloping　surface,　and　the　interval　reliability　index　decreases　with　the　damage　severity　increase　of　the　beam.