Abstract: The radiation directivity of a complicated conformal array of underwater acoustic transducers is presented based on the boundary element method. It includes the element directivity of each transducer, the natural beam pattern and the controlled beam pattern of the transducer array. At first, the boundary element model of the conformal array is built up, and then the boundary condition is exerted on the model according to the design and environment in which the transducer array is used, and the radiation directivity of the conformal array is calculated. An experiment has been done to measure the directivity in an anechoic water tank. The calculated and the experimental results are compared and analyzed. They are consistent to each other. It is shown that the boundary element method together with the detailed calculations is successful to simulate and predict the radiation directivity of an underwater acoustic transducer array.