A new model is presented for the development of stress during electromigration. Formally similar to a thermal stress model, it provides a method of calculating all of the components of the stress tensor and clearly couples vacancy transport and stress evolution with the boundary conditions that apply to the metal. Analytic solutions are discussed for electromigration either normal or parallel to a plate. The latter is similar to the metallization in experiments by Wang et al., permitting us to reinterpret these experiments. We find that the effective charge for vacancies in pure polycrystalline Al at 533 K is about 1.3. Using parameters that were either measured or calculated with the Embedded Atom Method, our model displays good agreement with both transient electromigration data and drift data.