The outstanding mechanical engineer professor H.M.Mushtary was the first director (1946 - 1972) of Kazan Physical Technical Institute, in which he was the chief of the Department of the Theory of Shells more than 30 years. Corresponding member of the Academy of Sciences N.G.Chebotarev has organized in 1946 Sector of Mathematics. Since the fiftieth years the main scientific direction of Sector of Mathematics has become the Theory of the Filtration. A valuable contribution to the development of mechanics at Kazan Physical Technical Institute was made by the famous scientists mechanical engineers K.Z.Galimov, G.Z.Salehov, M.A.Ilgamov, M.S.Kornyshin and others.

The Institute of Mechanics and Engineering of Kazan Scientific Center of the Russian Academy of Sciences is founded in accordance with the Resolution of the USSR Academy of Sciences Presidium No.165 dated the 28th May 1991 on the base of mechanics departments of Kazan Physical Technical Institute. Organizer and first Director (1991 - 1996) of the Institute was corresponding member of the Russian Academy of Sciences M.A.Ilgamov .

In 1996-98 the Acting Director of the Institute ​was Ph.D. (now Doctor of Technical Sciences) V.L. Fedyaev. In 1998, the Corresponding Member of the Russian Academy of Sciences D.A. Gubaidullin became the director of the Institute.

In 2013, the Institute was transferred to the Federal Agency of Scientific Organizations (FANO Russia).

In 2017, the institute was attached to the Kazan Scientific Center of the Russian Academy of Sciences. Currently, Institute of Mechanics and Engineering is a Subdivision of the Federal State Budgetary Institution of Science «Kazan Scientific Center of the Russian Academy of Sciences».

In the Institute the scientific researches on the dynamics of multiphase media, theory of shells, aerohydroelasticity, non-linear stability and control theory will be carried out.