Abstract:Thestabilityofhybridfiniteelementmethodoftransientthermalstressproblemishardtobeguaran-teedbecauseofthedifficultyofsatisfyingtheladyshenskaya-babuska-brezzi(LBB)conditions,accordingly,the combinedhybridfiniteelementmethodoftransientthermalstressproblemisproposed.Combinativevariation principleandthecorrespondingfiniteelementdiscretizationoftransientthermalstressproblemisconstructedon thebasisofdomaindecompositiontechnique.Thenumericalperformanceofcombinedhybridelementforsol-vingtransientthermalstressproblemisverifiedbynumericalexperiments.Thenumericalresultsindicatethat combinedhybridelementwith8nodes(CHH(0-1))cangivealmostthesamecomputingaccuracyofdisplace-mentandbettercomputingaccuracyofstresscomparedwithcuboidelementwith20nodes(B20). Keywords:transient;thermalstressproblem;combinativevariationprinciple;stability;combinedhybridele-ment;bigwidth-to-thicknessratio;stressaccuracy