The soft deposition of Cu clusters with Wulff-shape on an Au(001) surface is studied by constanttemperature molecular dynamics. The influence of the kinetic energy, the substrate, the temperature and the cluster orientation is analyzed. Bombardment energy ranges between 1 and 100 meV/atom. At low energy the deposition is mainly elastic, while at higher it is plastic. Randomly rotated clusters suffer a less violent collision. Only in some aligned clusters, epitaxia is found. In the rest of systems, the [00 1] axis of the cluster is at an angle of 45° to the same axis of the substrate. The temperature modifies the horizontal planes such that the Cu main grain matches to the substrate surface. The number of grains is larger in the aligned systems at low temperature.