Deterministic　damage　detection　methods　often　fail　in　practical　applications　due　to　ever-present　uncertainties.　Moreover,　vibration-based　model　updating　strategies　are　easily　affected　by　measurement　noises　and　could　encounter　ill-conditioning　problems　during　inverse　solutions.　On　this　account,　a　model-free　method　has　been　proposed　combining　modal　interval　analyses　with　static　measurements.　Structural　geometrical　dimensions,　material　parameters　and　external　loads　are　expressed　by　interval　variables　representing　uncertainties.　Mechanical　formulas　for　static　responses　are　then　extended　to　their　interval　forms,　which　are　subsequently　solved　using　classic　interval　and　modal　interval　analyses.　The　analytical　interval　envelopes　of　static　responses　such　as　deflections　and　strains　are　defined　by　the　interval　solutions,　and　damage　can　be　detected　when　the　measured　responses　intersect　the　envelopes.　By　this　approach,　potential　damage　can　be　found　in　a　fast　and　rough　way　without　any　inverse　solution　process　such　as　model　updating.　The　proposed　method　has　been　verified　against　both　numerical　and　experimental　reinforced　concrete　beams　whose　strains　were　taken　as　the　desirable　responses.　It　was　found　that　the　strain　envelopes　provided　by　modal　interval　analysis　were　narrower　than　those　by　classic　interval　analysis.　Modal　interval　analysis　effectively　avoids　the　phenomenon　of　interval　overestimation.　In　addition,　the　intersection　point　also　identifies　the　current　external　load,　providing　a　loading　alarm　for　structures.　©　2020　by　the　authors.