Geometries and energies for possible trapping sites of anthracene in hexagonal closed packed (hcp) argon matrices have been calculated and compared to corresponding trapping sites calculated for the face centered cubic fcc argon host. The random search method (RSM) has been applied which combines statistical and molecular dynamics (MD) components in the generation of initial geometries and their relaxation. A total of 1322 runs yielded 12 unique site structures. In none of them the anthracene is located in the {111}-plane of the host crystal, in contrast to the situation found for the fcc host structure.