We have analyzed the migration of spherical and cylindrical inclusions under a direct current and a thermal gradient in an infinite medium and near a planar boundary. Our study of inclusion motion in an infinite medium is concerned primarily with the application of the marker‐motion technique to measure mass transport in the lattice. It is shown that, in addition to the lattice motion, there are contributions to marker movement coming from mass transport by surface and volume diffusion, which is induced by the change of potential gradient on the marker surface. To measure the true lattice velocity, the marker used must be a good insulator compared to the matrix material, and its size should exceed a few microns. The study of inclusion motion near a boundary is for analyzing pore migration by electromigration in thin films. Three cases have been considered, which include a spherical pore near a plane and between two planes and a cylindrical pore connected to two planes. We concluded that the pore migration in the lattice is due to surface electromigration and the planar boundary generally increases pore velocity and distorts its shape during migration.