A possibility is analyzed to use direct drive cylindrical targets in the fast ignition mode irradiated by beams of nearly relativistic heavy ions with long ranges in matter. The minimum beam energy required to compress the DT fuel in a 1-cm-long target to (ρR)DT = 0.5 g/cm2, ρDT = 100 g/cm3 is found to lie in the range 10–15 MJ. Ignition and axial burn propagation is achieved with a 0.2-ns, 0.4-MJ pulse of 100-GeV heavy ions. Thermonuclear energy gains in the range 50–150 appear to be possible.