An apparatus for extracting air from within flexible packages having granular or otherwise flowable contents includes a package conveyor and a downwardly-open, vacuum extraction hood through which the packages are conveyed so that an upper portion of each package is moved through the extraction hood. The interior of the hood is joined in fluid communication with a vacuum source, so that air is extracted from within each package as it is conveyed through the hood. The present apparatus further includes a closing mechanism positioned immediately downstream of and in operative association with the extraction hood, whereby the upper portion of each package is maintained in a closed configuration prior to sealing, so that the interior of each package is not exposed to ambient conditions after it is conveyed out of the extraction hood, and prior to sealing of the upper portion.