Abstract: A plastic closure that comprises a cap having a base with a peripheral skirt defining the cap interior and threads on the skirt for securing the closure to a container. A liner is secured to the interior of the cap, preferably by being compression molded in situ on the base. The liner consists essentially of a multiplicity of alternating layers of a matrix polymer material such as EVA and a barrier material such as EVOH to resist transmission of gas, water vapor and/or flavorants through the liner. The matrix polymer material preferably is preblended with a compatibilizer material such as a maleic anhydride grafted polymer that ties the matrix polymer material to the barrier material.