Abstract: A capping machine for applying plastic screw-on caps (10) having a tamper evident band 38 to flexible sided round containers (12) having a neck provided with a radially extending flange (24) adjacent the open top of the container. The capping machine includes a portion (114) rotatable about a stationary portion (58), the rotatable portion including a plurality of operating stations (116). Each operating station has a chuck (118) and a novel gripping structure (120) capable of firmly engaging the flange (24) on the container to prevent the container from rotating when a cap is being screwed onto the container. The chucks and gripping structures are each provided with cam followers (122, 124) which engage cams (126, 128) and, as the rotatable portion (116) rotates about the stationary portion (58), the chucks and gripping structures will be shifted vertically in time with each other.