Using the embedded-atom method, the structure of small copper clusters on Au(111) electrodes has been investigated both by static and dynamic calculations. By varying the size of roughly circular clusters, the edge energy per atom is obtained; it agrees quite well with estimates based on experimental results. Small three-dimensional clusters tend to have the shape of a pyramid, whose sides are oriented in the directions of small surface energy. The presence of a cluster is found to distort the underlying lattice of adsorbed copper atoms.