Abstract: An evacuation actuating closure includes a lower cap member with a valve seat plate defining a plurality of angularly displaced venting holes at a central area. An annular guiding wall has upper and lower annular portions above and below the valve seat plate. The lower annular portion can be sealingly engaged with an annular upper wall of a container body. An elastomeric disc member includes an elastomeric central portion fixed on the valve seat plate, and a peripheral brim portion to block resiliently the venting holes. The venting holes are unblocked when the pressure below the venting holes is higher than that above the venting holes. An upper cap member includes a transverse depressing portion and an annular skirt portion sleeved on and slidably retained on the annular guiding wall so as to confine an air transit chamber above the valve seat plate. An elastomeric ring-shaped check valve member is disposed between the annular skirt portion and the annular guiding wall.