The Institute was founded on 5 November 1959 by the Decree of the Council of Ministers of the Georgian SSR (No. 750, 22 September), and was named the Institute of Machine Science.
The fpunding initiators of theInstitute were academicians 
Raphiel Dvali and 
Vakhtang Makhaldiani, whose research onmobile machines and engins running in mountain conditions provided a basis 
for the creation of the Institute and  used to build the institute and formulation of its main activity.
In 1970, the name of the institute was changed to the Institute of Machine Mechanics. Since 1994, the institute has been named after Rafiel Dvali. Since 2006, the institute has been established 
as a legal entity under public law - LEPL Rafiel Dvali Institute of Machine Mechanics.

 
    
 Rafiel Dvali (1972-1985)
                                  Vakhtang Makhaldiani (1959-1960)
 
From the day of its foundation until 1960, academician V. Makhaldiani was the Acting Director of the Institute.
In 1960-1961, the Director of the Institute was 
Giorgi Ambokadze, Candidate of Technical Sciences.

In 1961-1972, the Institute was led by 
Iovel Jebashvili, Candidate of Technical Sciences.

In 1972-1985, 
Rafiel Dvali, prominent Georgian scientist and public figure, academician of the Georgian Academy of Sciences was appointed Director of the Institute.
In 1985-1998, 
Iovel Jebashvili, Professor and corresponding member of the Georgian Academy of Sciences, was Director of the Institute again.
In 1998-2006, the Institute was led by prominent scientist 
Robert Adamia, academician of the Georgian Academy of Sciences.

Robert Adamia
From 2006 until today, Director of the Institute is Tamaz Natriashvili, academician of the Georgian National Academy of Sciences.