<p>An apparatus for capping containers comprises a primary suction member (31) for attracting the central portion of a cap (L) at the lowermost position within a cap stacker (11), and a secondary suction member (34) for attracting a peripheral portion of the cap. Although both the suction members are stretchable, the secondary suction member is contractable more greatly than the primary suction member when attracting the cap. Both the suction members attract the cap in the lowermost position within the stacker at the same time to withdraw the cap from the stacker, whereupon the secondary suction member contracts more greatly than the primary suction member to create a clearance between the attracted cap and another cap adjacent thereto immediately thereabove, permitting air to flow in between the two caps through the clearance to prevent occurrence of a negative pressure.</p>