Abstract
The cluster structures arising in continuum models of percolation are investigated with respect to the cluster anisotropy as function of the degree of space filling. It is shown that the smaller and intermediate sized clusters are anisotropic up to high degrees of space filling. The same holds for the largest cluster of the system up to the percolation threshold. At this point the percolating cluster becomes isotropic, indicating a qualitative change of cluster shape at the percolation transition.