The theoretical attenuation of tramc, noise by long barriers has been studied, by using a Monte Carlo snapshot technique for description of individual vehicle contributions, and the results compared with those obtained when line and point source approximations are used for the traffic noise source. The line source approximation is shown to give, in principle, the attenuation by a barrier of L,q rather than Lzo and to lead to an underestimate of the Llo attenuation. The use of a point source is shown to represent a complementary approximation to the line source method. A detailed calculation, for a particular motorway configuration, in which a stochastic line source model was used shows good agreement with the design curve of the Departmer~t of the Environment Design Bulletin 26 for path differences less than 0.5 m. At greater path differences the stochastic line source is found to predict a smaller attenuation of Llo than that predicted by DB 26. The validity, of the assumptions in the stochastic line source model is critically examined, and a design curve for Llo is given which extends the range of that found in Design Bulletin 26.