In this paper two problems in modeling electromigration are addressed. The first problem is an issue of principle concerning counting the number of variables and the number of equations for formulating a well-posed mathematical problem. The second problem deals with setting up a system of equations which are sufficiently detailed for performing computer simulations of the local dynamics governing electromigration phenomena, and which also keep the CPU consumption within acceptable limits. A model for electromigration, which is based on a fluid–gas picture for the material transport, is proposed for dealing with both questions. The flow of matter is described as a combined flow of lattice sites and a flow of vacancies. The gas component is used to describe the vacancy flux.