Because　of　the　presence　of　second-phase　particles　or　nanoscale　particles,　a　term　of　threshold　stress　incorporated　into　the　power-law　creep　model　of　some　materials,　such　as　magnesium,　aluminum,　and　chromium　alloys.　The　estimation　of　the　creep　crack-tip　stress　field　for　these　materials　is　notably　important　to　facilitate　their　exploitation　in　high-temperature　structures.　In　the　present　work,　a　two-term　asymptotic　expansion　of　the　stress　field　is　developed　to　predict　the　creep　crack-tip　stress　field　for　power-law　creep　materials　with　threshold　stress.　The　finite　element　method　is　used　to　verify　the　accuracy　of　the　two-term　asymptotic　expansion　of　the　stress　field.　The　simulation　results　reveal　that　the　two-term　asymptotic　expansion　of　the　stress　field　is　accurate　enough　as　an　engineering　method　in　estimating　the　creep　crack-tip　stress　field.　In　addition,　the　existing　estimation　method　of　the　time-dependent　C-integral　of　C(t)　can　be　directly　implemented　in　power-law　creep　materials　with　threshold　stress.　©　2021　Elsevier　Ltd