Circular rings of smooth muscle that can contract to regulate the movement of food through the gastrointestinal tract are called

Sphincter muscles

Explanation:

The circular rings of smooth muscles, that can contract to regulate the movement of the smooth muscles that can contract to regulate the movement  of food through the gastrointestinal tract are known as sphincter muscles.

These two layers are outer layer and inner layer. The outer layer is longitudinal and the inner layer is circular. They contract rhythmically to squeeze food.