Geometries and interaction energies for methane clusters with naphthalene and pyrene were studied. Estimated CCSD(T) interaction energies for the clusters at the basis set limit were -1.92 and -2.50 kcal mol(-1), respectively. Dispersion is mainly responsible for the attraction. Electrostatic interaction is very small. Although the benzene-methane cluster prefers a monodentate structure, in which a C-H bond of the methane points toward the benzene, the methane clusters with the polycyclic aromatic hydrocarbons do not prefer monodentate structures. In the benzene-methane cluster, the weak electrostatic interaction stabilizes the monodentate structure. On the other hand the dispersion interaction controls the orientation of methane in the naphthalene and pyrene clusters. The dispersion interactions in these clusters are significantly larger than those in the benzene-methane cluster. The methane prefers the orientation which is suitable for stabilization by dispersion. Hydrogen atoms of the methane locate above the centers of hexagonal rings of the polycyclic aromatic hydrocarbons in the stable structures. The structures have a small steric repulsion and this positions them only a short distance from the aromatic plane. The large dispersion contribution to the attraction shows that interactions between carbon atoms are mainly responsible for the attraction, and that hydrogen atoms are not important for the attraction. This shows that the interactions between the methane and polycyclic aromatic hydrocarbons are not pi-hydrogen bonds.