Stop signs used in the United States and most other countries are eight-sided octagons, the shape of which was initially proposed in 1923 by the Mississippi Valley Association of State Highway Departments. The red octagon is one of two stop sign shapes that are allowed under the Vienna Convention on Road Signs and Signals. The other shape is a red circle with a red inverted triangle within it, set on either a white or yellow background.
The Mississippi Valley Association of State Highway Departments shape recommendations were based on conveying a level of danger associated with the area where the sign was being placed. The a greater the number of sides, the higher the level of danger. They reasoned that since a circle technically has an unlimited number of sides, it should be used to show the highest level of danger (such as at a railroad crossing), with the eight-sided octagon, being the next highest, followed by the diamond, square and triangle.
In 1935, the Manual on Uniform Traffic Control Devices, which set nationwide road-sign standards, required stop signs to be yellow octagons. When this manual was revised in 1954, the color of the stop sign was changed to red.