Eshelby was elected a Fellow of the Royal Society in March 1974. He was awarded the Timoshenko Medal in 1977.
In 2012, the Eshelby Mechanics Award for Young Faculty and the Eshelby Memorial Bursary was founded in his memory. was launched to commemorate the memory of Eshelby. The award is given annually to rapidly emerging junior faculty who exemplify the creative use and development of mechanics, and awardees are formally recognised at the annual Applied Mechanics Division Banquet at the American Society of Mechanical Engineers' International Mechanical Engineering Congress and Exposition (ASME-IMECE) meeting.