By the Resolution of the Cabinet of Ministers of the USSR of June 18, 1991, No. 380, in commemoration of the 200th anniversary of the birth of the discoverer of non-Euclidean geometry, Nikolai Ivanovich Lobachevsky, a medal was established in honor of the outstanding scientist. Since 1992, according to the Regulation on the procedure for awarding the N.I. Lobachevsky medal, "the medal is awarded by the Academic Council of Kazan State University once every five years to Soviet and foreign scientists for outstanding work in the field of geometry." The competition is held simultaneously and jointly with the competition for the N.I. Lobachevsky Prize of the Russian Academy of Sciences; the jury of the competition includes representatives of the Russian Academy of Sciences and employees of Kazan University. Unlike the tradition of 1897-1903 (when 4 medals were awarded for 3 ceremonies), the medal is awarded not to the reviewers of the submitted works, but directly to their authors.
As of 2010, 4 medals have also been awarded in 3 ceremonies (1992, 1997, 2002).