Coutil (or Coutille) is wovencloth created specifically for making corsets. It is woven tightly to inhibit penetration of the corset's bones and resist stretching. Coutil has a high cotton content. Cotton has good dimensional stability, or a resistance to stretching, which makes it a good choice for such a stressed garment.
Coutil may be made to be plain (similar to 100% cotton facing), satin, or brocade. It is common for coutil to have a herringbone texture, or a similar woven texture.