Fundamental research in ultrasonic diagnostics is often limited by the relatively simple models of propagation invoked in what is largely an empirical science. Careful discussion of the problem reveals the need for more sophisticated propagation theories as the basis of measurement techniques and for the interpretation of experimental results. It is thus important for dialogue between theoreticians and experimentalists in the field. The complexity of ultrasonic wave propagation in tissue arises from a combination of factors. First, there is the biochemical sophistication of the media concerned. Second, there is the variety of physical phenomena involved: the diffractive nature of the ultrasonic field, the presence of absorption, the presence of large scale inhomogeneities and small scale scatterers, and the possibility of finite amplitude propagation effects. It has tended to be the custom to deal with each of these problems on an individual basis with a second feature being introduced as a perturbation of the results obtained for the first. The present authors have been concerned to find a unified approach which will permit each of the effects to be taken into account in relation to the others. This approach is based on the application of two-dimensional evolution equations modelling ultrasonic propagation in non-cavitating soft tissues. The model incorporates all the propagation phenomena known from experimental studies, indicating a need for knowledge of nine material parameters for a complete description. It thus provides a basis for numerical investigation of the relative significance of the parameters under different conditions. This will permit identification of those that should be known experimentally with high precision and those that have a minor role in the propagation phenomena.