The cavity growth behavior in a polycrystalline LSI conductor is investigated on the basis of diffusion along grain boundary (GB) and interface (IF) induced by stress and electric current. The of GB and IF, which strongly affects the characteristics of the atom migration. Numerical analysis is conducted for a polycrystalline conductor with GB/IF network after a discussion on a specialized FEM for the diffusion. Results obtained are as follows. (i) In a conductor, the atom migration is eminently activated near a cavity along GBs while there is little flow without the defect. (ii) IF diffusion between the conductor and the surrounded passivation activates the atom migration along GBs inside of a conductor. This implies that the cavity grows under the interaction between GB diffusion and IF one. (iii) Under an external stress, the cavity growth is fast in the early stage while it is decelerated by the constraint of the triple junction ahead of the cavity. (iv) The complex branches of the atom migration due to electric current (EM) amplifies the stress evolution and the stress-induced atom migration (SM) takes place. The cavity grows under the interaction between EM and SM, which stems from the GB/IF network.