Finite element solutions to problems of electromigration and stress-driven diffusion in polycrystalline films are presented. The numerical formulation accounts for diffusion along grain boundaries and through the bulk. The procedures are validated by comparing the finite element solutions to an existing analytic solution of an idealized, isolated grain boundary lying parallel to current flow. A simple polycrystalline interconnect is then considered and the effects of diffusion along each grain boundary and through the bulk are each added separately to the analysis so that the importance of each mechanism can be ascertained. In some cases, the inclusion of additional diffusion paths result in significant reductions in predicted stress levels.