Currently,　the　main　concerns　of　Pb-free　solder　joints　are　focusing　on　electromigration　(EM)　and　thermomechanical　fatigue　(TMF)　problems.　Many　models　have　been　established　to　understand　the　failure　mechanisms　of　the　joint　under　such　single　test　conditions.　Based　on　the　fact　that　almost　all　microelectronic　devices　serve　in　combination　conditions　of　fluctuated　temperature　and　electric　current　stressing,　the　coupling　effects　of　EM　and　TMF　on　evolution　of　microstructure　and　resistance　of　solder　joint　had　been　investigated.　The　failure　models　of　binary　SnBi　alloy　and　ternary　SnAgCu　(SAC)　solder　under　the　coupling　stressing　were　divided　into　four　and　three　different　stages,　respectively.　The　failure　mechanisms　were　dominant　by　the　relationship　of　phase　segregation,　polarity　effect,　phase　coarsening,　and　the　coefficient　of　thermal　expansion　mismatch.　Cracks　tend　to　form　and　propagate　along　the　interface　between　intermetallic　compound　layers　and　solder　matrix　in　SAC　solder.　However,　grain　boundary　was　considered　as　the　nucleation　sites　for　microcracks　in　SnBi　solder.　High　current　density　alleviates　the　deterioration　of　solder　at　the　beginning　stage　of　coupling　stressing　through　Joule　heating　effect.　An　abrupt　jump　of　resistance　could　be　observed　before　the　failure　of　the　joint.　The　failure　molds　were　determined　by　interactions　of　EM　behaviors　and　TMF　damages.　(C)　2013　American　Institute　of　Physics.　[http://dx.doi.org/10.1063/1.4789023]