An umbrella structure according to the invention includes a cover, a shaft, a notch, a runner, main ribs and stretchers. The notch is downwardly extended to form an extension section, which is accommodated with the runner and extruded to form an integral elastic protrusion. The protrusion is devised as a fastening button with one end thereof joined with the extension section, and a projecting top portion forming a supporting plane for butting against the runner. When the umbrella is stretched, the supporting plane of the protrusion section is butted against a lower section of the runner to stretch the umbrella.