Ultrasonic assessment of materials and defects are affected by microstructural parameters like grain size and texture. When a beam of ultrasound propagates in a polycrystalline medium, it undergoes extensive scattering by grains, grain boundaries and other microstructural features such as dislocations, voids, micro cracks etc. To understand the role of anisotropy and grain size distribution on an ultrasonic beam, a model system is proposed for carrying out ultrasonic wave propagation in a model characterized by grain size distribution and grain orientation distribution. A 2D polycrystalline medium constructed using Voronoi tessellations with a specific grain size distribution is considered and orientational averaging studies are carried out. © 2016 AIP Publishing LLC.