When people say that sheep wiggle their butt up and down when they walk, they are typically referring to the tail, not the buttocks. The motion is primarily the tail swinging side to side from moving up and down in step when the sheep moves. This tail motion, on some sheep, those with short hair or docked tails in particular can resemble that the back end is shaking. But sheep lack gluteal muscles that oscillate as obviously as people's, so they are not consciously shaking their butt. Any movement in your back is simply due to natural muscle shifts that occur when you walk.

The tail is wagging in part due to the cadence of the step. The tail also wags as the legs propel the movement. Tail flicking can occur when the sheep is alert or interested in something. Ewes with new babies will wag their tails like crazy, especially the lambs feeding. It's a hefty answer, which is often associated with stuffing.

Sheep don’t all express this movement in the same way. Breeds which retain a full tail, such as some traditional or feral sheep, demonstrate the tail articulation more clearly. In the commercial situation, many sheep have docked tails, so the tail motion is less apparent or virtually non existent.

If you see a sheep whose butt appears to wobble as it walks, you’re probably just seeing regular tail action.