Described is a packaging material which contains a matrix material coated with a thermoplastic polymer and an effective absorbing amount of a cyclodextrin material. The cyclodextrin material is selected from the group consisting of an -cyclodextrin, a -cyclodextrin, a -cyclodextrin or mixtures thereof. The packing material can act as a barrier with respect to permeants, such as water vapor, aromatic and aliphatic hydrocarbons, monomer compositions and residues, off odors, off flavors, perfumes, smoke, pesticides, toxic materials, etc. The barrier properties of the cyclodextrin material may be altered by modifying the moisture content of the cyclodextrin material prior to incorporating into the matrix material.