Abstract: A roller for an semiautomatically or automatically actuated tire mounting and demounting machine flexibly equipped for mounting tires on rims of all configuration, said mounting machine comprising working elements which mount a resiliently composed tire on a rim. The roller herein may also be used in connection with semiautomatically operated tire mounting and demounting tools, and other types of tire mounting machines in which a roller is utilized. The roller herein has upper and lower portions respectively of which lower portion is shaped in the form of an inverted truncated cone, and integrally situated on the top of such lower portion is a circular member of a diameter which is larger than any part of the lower portion of such roller.