The institute was established in 1956 as the
Sverdlovsk Division of the
Steklov Institute of Mathematics. Its building at 16 S. Kovalevskaya Street was laid in 1957 and put into operation in 1961. In 1970, the division was transformed into the Institute of Mathematics and Mechanics of the Academy of Sciences of the USSR.
After Academician N.N. Krasovskii's death in 2012, the institute was given his name. The institute works under the scientific and methodological leadership of the Division of Mathematical Sciences of the RAS and the Division of Mechanics and Control Processes of the RAS.
Throughout its history, the institute was headed by Academician S.B. Stechkin, Academician N.N. Krasovskii, Academician A.B. Kurzhanskii, Prof. Dr. V.D. Batukhtin, Academician Yu.S. Osipov, Academician A.F. Sidorov, and Academician V.I. Berdyshev. Currently, Prof. Dr. N.Yu. Lukoyanov is Director of the institute.
The Krasovskii Institute of Mathematics and Mechanics is the publisher of the quarterly journal
Trudy Instituta Matematiki i Mekhaniki UrO RAN (its English translation is published as supplement issues of the
Proceedings of the Steklov Institute of Mathematics) and the semi-annual online Ural Mathematical Journal.