Non-destructive evaluation (NDE) of elastic modulus in materials has broad applications in fields such as geological exploration, quality evaluation and medical diagnosis. A key to these techniques is to solve the inverse problem of identifying the distribution of elastic modulus. While conventional theories and numerical methods often involve solving multiple variational problems iteratively for each individual case, the demand of real-time response and high-throughput application of NDE is growing, especially for advanced manufacturing and clinical practices. To address this challenge, in this project, we leverage some of the recent progress in data science and propose a deep learning (DL) approach to solve the inverse problem of modulus identification in elasticity for high accuracy and efficiency.