An improved strap adapted to be worn adjacent the skin is made up of an elastic ribbon having flexibility in the longitudinal direction and limited lateral flexibility. A soft padding covers the elastic ribbon, and a smooth-faced material outer covering encloses both. The components of the strap are attached along the longitudinal edges of the strap to form a smooth-faced material surface with undulations (wrinkles) permitting limited longitudinal stretching of the elastic strap to produce a smooth strap surface during wear. The elasticized strap material makes up a major portion of the strap which, preferably, also includes non-elasticized end portions for attachment to garments, clips, etc.