FASAwas founded in 1972, by Mary A. Hieckman, an art teacher from Houston who had retired to Somerset. The group was originally known as the Creative Stitchers. Groups formed at the same time in Houston and Dallas, later giving birth to the statewide group. After a few years, all the individual chapter names were changed to 'Fiber Artists' to more accurately reflect the types of artistic work being produced by members.

Today FASA has grown from 17 original members to more than 150 at present.

The Fiber Artists of San Antonio group is a member of the Texas Fiber Federation. Other Federation groups exist in Dallas and Houston.

Every two years, an individual chapter sponsors a statewide conference and exhibition of Fiber Art. The first conference was held in 1978. In 2004, the statewide conference was sponsored by the Houston Area Fiber Artists and held in Clear Lake, Texas.

The next statewide conferences will be held in 2006 in San Antonio and sponsored by the Fiber Artists of San Antonio.