Electromigration　(EM)　becomes　one　of　the　most　challenging　reliability　issues　for　current　and　future　ICs　in　10-nm　technology　and　below.　In　this　article,　a　novel　method　is　proposed　for　the　EM　hydrostatic　stress　analysis　on　2-D　multibranch　interconnect　trees,　which　is　the　foundation　of　the　EM　reliability　assessment　for　large-scale　on-chip　interconnect　networks,　such　as　on-chip　power　grid　networks.　The　proposed　method,　which　is　based　on　an　eigenfunction　technique,　could　efficiently　calculate　the　hydrostatic　stress　evolution　for　multibranch　interconnect　trees　stressed　with　different　current　densities　and　nonuniformly　distributed　thermal　effects.　The　proposed　method　solves　the　partial　differential　equations　of　transient　EM　stress　more　efficiently　since　it　does　not　require　any　discretization　either　spatially　or　temporally,　which　is　in　contrast　to　numerical　methods,　such　as　the　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　convergence　of　the　proposed　method　is　demonstrated　by　numerical　experiments　on　practical　power/ground　networks,　showing　that　only　a　small　number　of　eigenfunction　terms　are　necessary　for　the　accurate　solution.　Thanks　to　its　analytical　nature,　the　proposed　method　is　also　utilized　in　efficient　EM　analysis　techniques,　such　as　searching　for　the　void　nucleation　time　by　a　modified　bisection　algorithm.　The　numerical　results　show　that　the　proposed　method　is　10X-100X　faster　than　the　finite　difference　method　and　scales　better　for　larger　interconnect　trees.