Radon transforms can be used to decompose seismic shot records into sets of plane waves and, as such, are a useful processing tool. Haneveld and Herman (1990) discussed a fast algorithm for the numerical evaluation of both the forward and inverse 2-D Radon transforms. They showed that, by rewriting the transform as a convolution, the computation time is proportional to Nlog2N, instead of N2 (where N denotes the number of input and output traces). In the present paper, we describe a similar method for the computation of the 3-D Radon transform for the case of rotational symmetry (see also Mallick and Frazer, 1987; McCowan and Brysk, 1989). With the aid of asymptotic techniques, the 3-D Radon transform is recast into a form similar to the 2-D Radon transform after which similar acceleration techniques are used. We have implemented and tested the fast transform on synthetic as well as on real data and found that the computation time of the fast 3-D Radon transform is indeed proportional to Nlog2N.