This paper describes work done in the course of a project to develop a computer model to simulate the behaviour of the mains LV distribution network at VLF communication frequencies. This was required in order to assist in the design and development of a mainsborne communication system. It has also helped to establish a theoretical understanding of the behaviour of the network. The cables of the network are modelled as three-phase transmission lines, their behaviour being analysed by means of the theory of normal modes. The modes employed in this project are different from those used conventionally for symmetric lines, The loads on the network include the distribution transformer, the street lamps, and the consumers' installations, of which the latter are the most significant. It has been discovered that many loads exhibit series resonance, due to the wiring inductance and the capacitance of many domestic appliances. A computer program has been written to model the network, treating it as a ‘tree’, with branches radiating from the signal transmitter. This program has been used with some success to simulate signal propagation on several distribution networks, giving results which agree quite well with measurements on those sites. However, the loads on the network are nondeterministic, since they depend on the appliances in each installation. Hence statistical techniques are required to characterise and to determine the signal propagation. This paper describes the use of the mean, standard deviation, and the normalised autocovariance function (NACVF) of the propagation characteristics for this purpose.