We discuss a new method for seismically imaging mantle plumes by modeling the plume as a vertical elastic cylinder and analyzing the effects of the cylinder on an incoming teleseismic plane wave. The incident plane wave decomposes into cylindrical waves for which the scattering coefficients can be computed by imposing continuity of stress and displacement at the cylinder boundary. We extended this development to cylinders with gradational boundaries by numerically integrating the elasto--dynamic equations. Synthetic seismograms calculated using this technique for a cylinder with a range of parameters appropriate for a mid-Pacific mantle plume (epicentral distance Δ=50¿--90¿, ΔT=200--400 K, boundary width=0--60 km) have the following characteristics: (1) a delay of the P wave arrival for an observational point directly behind the plume, (2) the focusing of energy into the region directly behind the plume where the focal length is ~2 times the plume diameter, and (3) the presence of secondary phases, and especially the excitation of a transverse component whose amplitude is up to 25% of the radial amplitude. Most of the phases arise from P-to-S conversions and reflections at the boundary of the cylinder. Increasing the epicentral distance reduces the focal length and strengthens the focusing effect for receivers near the plume. Increasing the thermal anomaly reduces both the focal length and the amplitude of the secondary phases. Using gradational boundaries does not affect the scattering of low-frequency waves, but it does cause the reduction or disappearance of the secondary arrivals at high frequency because of the reduced efficiency of the conversions. Synthetic seismograms for an incident S wave arrival show a time delay more than twice as long as for the P wave and stronger focusing but only weak secondary phases. Considerable coupling takes place between SV and SH. On the basis of these findings we outline an observational program to image the Hawaiian plume: stations should preferably be installed close to but not directly on top of the most likely position of the plume axis. ¿ 1998 American Geophysical Union