A two-dimensional model of Josephson junction of overlap type is presented. The energy input is provided through induced magnetic fields modeled by a set of boundary conditions. In the limit of a very narrow junction, this model reduces to the one-dimensional model. Further, an equation derived for the critical current leads in this limit to the critical current obtained from the one-dimensional model. Comparisons between stationary fluxon velocities obtained from the two models by means of numerical computations show that the difference is negligible. This supports the experimental observation that measurements are insensitive to the width of the junction. Journal of Applied Physics is copyrighted by The American Institute of Physics.