To provide a method and an apparatus for cuting a sliver during can changeover, especially, surely cutting the sliver by a simple means on design.

In a method of cuting a sliver, when can changeover of a drawing frame having a means receiving a sliver (22) in a can (24), a space between a sliver feeder, such as the outlet of a coiler plate (23), and the highest layer of the sliver in the following can is so expanded as the sliver is almost ruptured. To provide a method enabling surely cutting the sliver with a simple means on design, draft is increased at a draft zone (b) set at the front stage of a sliver outlet so as to start can changeover when a thin layer part 12' is provided in a overlap sliver and the thin layer comes at the outlet zone of the sliver outlet of a coiler plate.