External ring dampeners are made of the same plastic as the drum heads. The rings lie just inside the counter hoops, and sit flush against the drum head. External ring dampeners are used for the snare drum and the roms, but are not suitable for the bass drum.
When using external ring dampening on the snare drum it is a good idea to stick some tape between the dampening ring and the counter hoop. This allows you to fold back the dampening when you desire full sustain from the snare drum.