Understanding the propagation and scattering of ultrasonic waves within polycrystalline materials is relevant to both material characterisation and flaw detection NDE. Validating analytical theories of scattering however has historically been hampered by the difficulty of obtaining sufficiently reliable experimental data where the statistical properties of the grains within the volume of the material are known well enough. Instead, this presentation exploits important recent progress in numerical modelling, which for the first time enables accurate three-dimensional simulations of wave propagation and scattering in polycrystals. The presentation reports work using such a model to compare and validate 3D numerical simulations of wave scattering against existing analytical theories. A wide range of wavenumber to grain size ratios, ka, are considered such that scattering within the Rayleigh, transitional, and stochastic regimes are compared. The numerical calculations are based on an established Voronoi algorithm to generate statistically representative random materials. An explicit Finite Element scheme (Pogo) running on an array of graphics processors is used to solve the time-domain wave propagation problem. It is found that near perfect agreement exists with the generalized second order theories (type of Stanke-Kino) for attenuation coefficient when these theories are implemented with properly fitted second order material statistics.