Thispaperpresentsanewstrategyofusingtheradialintegrationboundaryelementmethod(RIBEM)tosolvenon-homogeneousheatconductionandthermoelasticityproblems.Inthemethod,theevaluationoftheradialin-tegralwhichisusedtotransformdomainintegralstoequivalentboundaryintegralsiscarriedoutonthebasisofelementalnodes.Asaresult,thecomputationaltimespentinevaluatingdomainintegralscanbesavedconsiderablyincomparisonwiththeconventionalRIBEM.Threenumericalexamplesaregiventodemonstratethecorrectnessandcomputationalefficiencyoftheproposedapproach.