This thesis describes the numerical modelling of bioacoustic structures, the focus being the outer ear or pinnae of the Rufous Horseshoe bat (Rhinolophus rouxii). There have been several novel developments derived from this work including: • A method of calculating directionality based on the sphere with a distribution of measuring points such that each lies in an equal area segment. • Performance estimation of the pinna by considering the directionality of an equivalent radiating aperture. • A simple synthetic geometry that appears to give similar performance to a bat pinna. The outcome of applying the methods have yielded results that agree with measurements, indeed, this work is the first time TLM has been applied to a structure of this kind. It paves the way towards a greater understanding of bioacoustics and ultimately towards generating synthetic structures that can perform as well as those found in the natural world.