A snap closure for a flexible, gusseted package and a flexible gusseted packing including the closure. The package includes a mouth portion arranged to be opened to provide access to the contents of the package. The package is formed of a flexible material and includes a front panel, a rear panel, and a pair of opposed side gussets. The panels and gussets each include a top portion, which between them define the package's mouth. The package's mouth is initially sealed but arranged to be opened, e.g., peeled apart. The snap closure enables the resealing of the mouth of the package and is made up of a pair of elongated elements, one of which includes a tongue extending along the length of it. The other element includes an undercut groove extending along the length of it. The elements are arranged to be pressed together, whereupon the tongue of the one element enters the groove of the other element with portions of the panels and side gussets tightly interposed therebetween. The closure elements may be a part of the package or a separate component for use therewith. In any case when the closure is utilized it recloses the mouth of the package to preclude or minimize the ingress of air into the package.