The behavior of unsteady wake vortices for the two-dimensional flat plate is simulated by a discrete vortex method. The flat plates and their wakes are represented by vortex sheets. The vortex sheets are replaced with discrete vortices. The freely deforming wake sheets are computed as a part of solution and the ground effect is included by a image method. In order to predict wake shapes accurately and to model closely coupled aerodynamic interference, a vortex core model and a vortex core addition scheme are used. The simulated wake shapes convecting behind the plates in unsteady motion are compared to a flow visualization result and other numerical results. The present results agree well with them. The present method is also applied to the aerodynamic analysis of flat plates in tandem configuration in ground effect.