A valve for a reclosable container comprises first and second opposing layers of a film material, wherein an overlap region of the second layer overlaps the container, and the first layer is sealed to the second layer around a portion of the second layer. The second layer is sealed to the container around a periphery of the overlap region, and opposing surfaces of the first and second layers form a substantially airtight seal therebetween upon direct contact of the layers. First and second offset apertures extend through the first and second layers, respectively. One of the first and second apertures is in fluid communication with an interior of the container and the other of the first and second apertures is in fluid communication with an exterior of the container. Vacuum pressure disposed over both of the first and second apertures causes the first layer to separate from the second layer to allow air to exhaust from the container.