The present article addresses the development at Centre for Non-destructive Evaluation, Indian Institute of Technology Madras, of three different numerical methods, namely finite element, ray tracing and finite-difference time-domain methods for investigating the propagation of ultrasonic waves through polycrystalline media. These methods are believed to aid in better understanding of ultrasonic wave interaction in materials exhibiting both simple and complex grain morphologies. The understanding is expected to provide an improved non-destructive assessment of material and defect characterisation. © 2019, The Indian Institute of Metals - IIM.