Numerical simulation studies are reported which provide insight into the origin of complex ultrasonic wave propagation phenomena observed in titanium alloys, rendering the nondestructive evaluation (NDE) measurements more difficult than in materials with simpler microstructure. This is of particular importance in the inspection of aero-engine rotating components because of the possibly catastrophic consequences of failure. The underlying phenomena is the distortion of the beam as it propagates through the material, causing both amplitude and phase modulations with respect to the beam that would exist in an isotropic, homogeneous media. Practical consequences include fluctuations in the signals produced by reflections from calibration reflectors such as flat bottom holes and back surfaces and an apparent excess attenuation implied by the mean values of these signals. The cause of these phenomena has long been believed to be the duplex nature of the microstructure of titanium alloys, which includes large-scale features such as prior beta grains, and small-scale features such as colonies. The purpose of the simulations is to guide a better understanding of the dependence of the experimental phenomena on both the experimental parameters and the microstructure features;The simulation is based on an interdisciplinary approach combining tools from applied mechanics and materials science. The microstructure is described by a generalization of the Potts model to the case of duplex microstructures. The wave propagation is treated by a numerical solution to a 2D scalar wave equation, which explicitly treats the multiple scattering phenomena believed to be playing a key role in controlling the experimental phenomena. These two tools have been joined to provide a self-consistent simulation package which qualitatively predicts many phenomena that have been observed experimentally. Included are the observations that signal fluctuations are minimum and apparent attenuation is greatest when a beam is focused near the reflector, signal fluctuations are greatest and backscattering is lowest when beams propagate parallel to directions with microstructure elongation, and apparent attenuation is lowest when the beam has traveled a greater propagation distance. The use of the model to verify a simple approach to parameterize the beam distortion is also reported.