The ISTAM was established in 1955 by the think tanks of the post independent India with its headquarters at IIT, Kharagpur. The society was formed with the idea of providing a common platform to the scientists, technologists and the engineers to share and discuss the current research work conducted by them individually or in groups to seek the solutions to the emerging problems for better living conditions. During the congress, five memorial lectures in honor of B.R. Seth, P.L. Bhatnagar, B. Karunesh, A.S. Gupta and G.I. Taylor are given by eminent researchers and also several invited lectures are arranged to cover the current trends of various topics in Theoretical and Applied Mechanics. The Annual Congress of the Society has been held at various IITs, NITs, Universities, Engineering colleges and other reputed research establishments in different parts of the country.

NIT Warangal is a public technical and research university located in Warangal, Telangana State, India. It is recognized as an Institute of National Importance by the Government of India. The foundation stone for this institute was laid by the then Prime Minister Jawaharlal Nehru in 1959, the first in the chain of 31 NITs (formerly known as RECs) in the country. The institute was renamed as the National Institute of Technology, Warangal in 2002. The Institute organized the 23rd and 44th ISTAMs in the years 1978 and 1999, respectively.