Recently, a governing parameter for electromigration damage, AFD*gen, was identified and, utilizing the parameter, a prediction method of electromigration failure was developed for the passivated polycrystalline line. The parameter AFD*gen was formulated considering the divergence of atomic flux due to electromigration in grain boundary network, and the boundary condition of metal line ends was not taken into account. So far, therefore, failure prediction was exclusively done for the metal line connected by electric-current input/output pads at both ends, not for the line connected by vias at both ends. It is known that there is threshold current density, jth, below which no electromigration damage appears, in the line connected by vias. In this study, first, a governing parameter for electromigration damage on the ends of passivated polycrystalline line is expressed considering the boundary condition of line ends concerning the atomic diffusion. Next, the way to estimate the threshold current density of the metal line with vias is shown based on the numerical simulation using the governing parameter.