In cellular radio communication systems, the concept of maximum packing is used for dynamic channel assignment. An H-packing of a graph G is a set of vertex disjoint subgraphs of G, each of which is isomorphic to a fixed graph H. The maximum H-packing problem is to find the maximum number of vertex disjoint copies of H in G called the packing number denoted by λ(G, H). In this paper we determine the maximum H-packing number of hexagonal networks when H is isomorphic to P 6 as well as K 1,3.