A numerical model has been developed to simulate propagation of ultrasonic beams in inhomogeneous moving media. The model is based on the ray theory of propagating waves, valid in the limit of high frequencies. The resulting equations depend only on local values of the velocity field and the speed of sound. In its implementation, the model assumes that the interactions of sound with the surrounding flow field are decoupled. This allows for applying the model in a post processing mode to flows computed by other means. The model was used to investigate beam behavior in unsteady cavitating flows. The study was motivated by reports of cavitation occurring in mitral bi-leaflet mechanical heart valves. The flow field and cavitation physics were simulated using a general purpose computer code, CFD-ACE. The ultrasonic beam model was then used to calculate the beam path, orientation, and frequency changes in the transient cavitating region. Results show that the presence of cavitation can fundamentally alter the beam propagation characteristics. Simple models that assume rectilinear propagation cannot, by definition, handle such flows. Cavitation incurs very large variations in the local sound speed, which in turn can induce very large distortions in the beam. This fact has strong ramifications regarding the accuracy of ultrasonic velocimetry when simple models are used to interpret Doppler data gathered under such flow conditions.