The invention relates to a method for producing self supporting container parts, such as dishes or covers, for containers for foodstuffs to be treated in a microwave oven, said containers each comprising at least one compartment for receiving the foodstuffs, along at least part of the circumferential surface of which compartment a microwave-radiation influencing material layer is provided in the wall of at least one associated container part, comprising the steps of providing a multilayer foil comprising said microwave radiation-influencing material layer and at least one material layer that does not influence microwave radiation, which is bonded thereto on at least one side of the microwave radiation-influencing material layer, bonding one side of the multilayer foil to a remaining portion of the container part in question, in such a manner that the material layer of the multilayer foil that does not influence microwave radiation is present on a free surface of the container part. The invention furthermore provides a container part thus produced, a method for producing a multilayer foil provided with holes and a multilayer foil thus produced.