The work arose from the practical need, a few years ago, to reduce the side lobes of a particular 47 kHz sonar transducer, used for acoustic fish target strength measurements. It has led to the development of a computational method of predicting the directional patterns of transducers with one or two side baffle plates. The method has been applied to the above-mentioned transducer and satisfactory agreement found between computed and measured results. Most of the latter are more recent ones but good agreement was also found when computations were made for baffle arrangements for which measurements were published in 1972. It is concluded that the method can now be used with confidence for the design of any future transducers or arrays with side baffles to reduce side lobe levels.