The　geometric　and　material　parameters　of　real-world　structures　always　contain　uncertainties.　Sometimes　such　uncertainties　should　be　quantified　when　precise　analyses　of　structural　computational　models　are　required.　An　inverse　problem　for　identifying　interval　parameters　has　been　developed　in　this　study.　The　relationships　of　mid-values　and　radii　between　interval　parameters　and　responses　were　first　established　using　Taylor　series　expansion.　Then　two　inverse　problems　were　formed　to　identify　the　mid-values　and　radii　of　parameters　in　a　successive　way.　By　this　means　the　phenomenon　of　interval　overestimation　was　maximally　avoided　and　the　process　of　inverse　optimization　was　highly　simplified.　The　proposed　method　has　firstly　been　verified　against　a　numerical　mass-spring　system.　Subsequently　using　the　measured　modal　data　of　a　set　of　steel　plates,　the　intervals　of　the　geometric　and　material　parameters　of　the　plates　were　identified.　The　analysis　results　demonstrate　that　the　method　provides　satisfactory　accuracy　and　precision　in　solving　interval　inverse　problems.　Interval　overestimation　can　be　effectively　restrained.　Therefore,　the　method　can　be　applied　to　solving　practical　engineering　problems　having　interval　uncertainties.　©　2015,　Editorial　Office　of　Chinese　Journal　of　Computational　Mechanics.　All　right　reserved.