Let　{(ξni,　ηni),　1　≤　i　≤　n,　n　≥　1}　be　a　triangular　array　of　independent　bivariate　elliptical　random　vectors　with　the　same　distribution　function　as　(S1,ρnS1+1−ρn2S2),ρn∈(0,1),　where　(S1,　S2)　is　a　bivariate　spherical　random　vector.　For　the　distribution　function　of　radius　S12+S22　belonging　to　the　max-domain　of　attraction　of　the　Weibull　distribution,　the　limiting　distribution　of　maximum　of　this　triangular　array　is　known　as　the　convergence　rate　of　ρn　to　1　is　given.　In　this　paper,　under　the　refinement　of　the　rate　of　convergence　of　ρn　to　1　and　the　second-order　regular　variation　of　the　distributional　tail　of　radius,　precise　second-order　distributional　expansions　of　the　normalized　maxima　of　bivariate　elliptical　triangular　arrays　are　established.　©　2018,　Institute　of　Mathematics,　Academy　of　Mathematics　and　Systems　Science,　Chinese　Academy　of　Sciences,　Chinese　Mathematical　Society　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.