A fabric strap may be used to attach a wearable electronic device to a user's body. The fabric strap may include a stretchable inner fabric layer formed from mesh fabric. A first set of ribs may be formed on a first side of the inner fabric layer and a second set of ribs may be formed on a second opposing side of the inner fabric layer. Load-modifying structures may be located in the ribs and may be used to increase the initial force required to stretch the strap, while allowing additional elongation to occur without requiring increasing force once a certain elongation percentage is reached. The load-modifying structures may be located in upper portions of the ribs and/or may span across openings in the ribs, and may include stitching, stiffeners, fabric layers, metal or plastic materials, spring members, and/or other structures.