This paper describes a three-dimensional (3-D) overlapping finite-element scheme for modeling movement in electromagnetic devices, which results in a continuously changing air gap. The method uses separate finite-element meshes to model the individual parts of the device. These meshes are coupled together electromagnetically on an interface using the Lagrange sliding interface technique. Treatments of overlapping mesh volumes are also discussed. The method was used to model a jumping eddy-current disc experiment. The results of the simulations compared favorably with measurements.