The present invention relates to a fluid tight tape for a perforable package or packet, which perforable package or packet is particularly suitable for containing under vacuum foodstuff to be thermally treated, comprising: a laminar body (2), made of elastically deformable material and resistant to relatively high temperatures, designed to be applied to the perforable package or packet suitable for containing the foodstuff to be thermally treated; a glue means (4) provided at one face of the laminar body (2) facing, in use, the package or packet, the glue means (4) being designed to make the laminar body (2) tightly adhere to the package or packet, the laminar body (2) having a bare area (5), lacking glue, at which a through opening (6) is obtained. The fluid tight tape comprises an elastic insert member (7) tightly housable in and anchorable to the through opening (6) of the laminar body (2), the elastic insert member (7) being designed to remain, in use, adjacent to or in contact with the package or packet with no interposition of the glue means (4).