In　some　alloys　such　as　9%Cr　heat　resistant　steels　and　magnesium　alloys,　the　creep　constitutive　equation　of　the　power-law　requires　a　term　of　threshold　stress　due　to　the　presence　of　second　phase　particles.　It　is　necessary　to　establish　an　estimation　method　of　C∗　for　such　alloys　to　predict　the　life　of　their　components.　In　this　paper,　the　General　Electric/Electric　Power　Research　Institute　(GE/EPRI)　method　and　the　reference　stress　method　were　modified　to　estimate　C∗　for　power-law　creep　materials　with　threshold　stress.　The　finite　element　method　was　used　to　verify　the　accuracy　of　the　modified　methods.　The　accuracy　of　the　calculation　equation　of　C∗　in　the　American　Society　for　Testing　Materials　(ASTM)　E　1457　was　also　assessed.　The　results　indicated　that　the　modified　GE/EPRI　method　was　sufficiently　exact　as　an　engineering　method.　h1　was　slightly　affected　by　the　applied　load　and　significantly　affected　by　the　threshold　stress.　The　accuracy　of　the　modified　reference　stress　method　increased　with　increased　applied　load　and　was　within　±40%.　The　accuracy　of　the　calculation　equation　of　C∗　in　ASTM　E　1457　was　not　affected　by　the　threshold　stress　and　the　equation　could　be　directly　used　for　power-law　creep　materials　with　threshold　stress.　©　2018　Elsevier　Ltd