Here is the list of some of the Institutes of India which offers PhD Mechanical Engineering course

Indian Institute of Technology Gandhinagar
Indian Institute of Technology, Hyderabad
Indian Institute of Technology, Iit Indore
Indian Institute of Technology, IIT Patna
Indian Institute of Technology, IIT Ropar
National Institute of Engineering
National Institute of Technology
National Institute of Technology (NIT) Silchar
B S Abdur Rahman University
B.S. Abdur Rahman Crescent Engineering College
B.V.B. College of Engineering & Technology
Bharati Vidyapeeth University College of Engineering
Coimbatore Institute of Engineering and Information Technology
Coimbatore Institute of Technology
College of Technology
Dayananda Sagar College of Engineering.
Defence Institute Of Advanced Technology,
Delhi Technological University
Gautam Buddha University
Gitam Institute of Technology
Government Engineering College
Hindustan Institute of Technology And Science
Hindustan University
Indira Gandhi National Open University, Regional Centre, Port Blair
K L E Society’s Sheshgiri College of Engineering & Technology
Kumaraguru College of Technology
M.M. Engineering College
M.M. University Institute of Engg & Technology
Nitte Mahalinga Adyantaya Institute of Technology
Noorul Islam Polytechnic College
Paavai Engineering College
Pandit Dwarka Prasad Mishra Indian Institute of Information Technology, Design And Manufacturing
Pondicherry Engineering College
Reva Institute of Technology and Management
S.N.S. College of Technology
Sardar Patel College of Engineering
Sardar Vallabhbhai National Institute of Technology
School Of Mechanical And Building Sciences
Shaheed Bhagat Singh College of Engineering & Technology
Sharda University
Shrama Sadhana Bombay Trusts's College of Engineering And Technology
Siddaganga Institute of Technology
Sinhgad College of Engineering
University Visveswaraya College of Engineering
Vishwakarma Institute of Technology