Electromigration　(EM)　becomes　one　of　the　most　challenging　reliability　issues　for　current　and　future　ICs　in　10nm　technology　and　below.　In　this　paper,　we　propose　a　new　analsys　method　for　the　EM　hydrostatic　stress　evolution　for　multi-branch　interconnect　trees,　which　is　the　foundation　of　the　EM　reliability　assessment　for　large　scale　on-chip　interconnect　networks,　such　as　power　grid　networks.　The　proposed　method,　which　Is　based　on　eigenfunctions　technique,　could　efficiently　calculate　the　hydrostatic　stress　evolution　for　multi-branch　interconnect　trees　stressed　with　different　current　densities　and　non-uniformly　distributed　thermal　effects.　The　new　method　can　also　accommodate　the　pre-existing　residual　stresses　coming　from　thermal　or　other　stress　sources.　The　proposed　method　solves　the　partial　differential　equations　of　EM　stress　more　efficiently　since　it　does　not　require　any　discretization　either　spatially　or　temporall,　which　is　in　contrast　to　numerical　methods　such　as　finite　difference　method　and　finite　element　method.　The　accuracy　of　the　proposed　transient　analysis　approach　Is　validated　against　the　analytical　solution　and　commercial　tools.　The　efficiency　of　the　proposed　method　is　demonstrated　and　compared　to　finite　difference　method.　The　proposed　method　is　10X　similar　to　100X　times　faster　than　finite　difference　method　and　scales　better　for　larger　interconnect　trees.