Abstract This work presents a numerical means of investigating the acoustic scattering by disk-shaped bodies. On the basis of Burton and Miller's method, the singularity-free formulations of Helmholtz integral equation and its normal derivative are used to form a composite equation. A triangle polar co-ordinate transformation method is further applied to treat the nearly singular kernels arising from a situation in which the field points and source points are very close together. Numerical simulations consist of the acoustic scattering by a short circular cylinder and a thin circular disk respectively. For the latter case with zero thickness, the corresponding analytical solutions involving angular and radial oblate spheroidal wave functions are evaluated as well. Comparing the numerical results with the experimental data and analytical solutions demonstrates the effectiveness of the proposed method.