Following a summary of the basic principles of 3D waveguide mesh modelling and the context of its application to room acoustic simulation, this paper presents a detailed analysis of the tetrahedral mesh topology and describes its implementation on a parallel computer model. Its structural characteristics are analysed, with particular emphasis on how they influence execution speed. Performance deterioration due to communication overhead in the parallelised model is discussed. Theoretical predictions are compared with data from performance tests carried out on different computer platforms and both are contrasted with the corresponding results from the rectilinear model, in order to assess the practical efficiency of the model. Objective validation tests are reported and discussed.