An electric power steering apparatus having a rack shaft supported at opposite end portions thereof by a rack-and-pinion mechanism and a ball-screw mechanism, respectively, includes a plain bearing slidably fitted around a rack shaft to support an intermediate portion of the rack shaft. The plain bearing thus provided considerably reduces a support span of the rack shaft and, hence, shifts a resonance frequency of the rack shaft to a higher frequency range. The rack shaft is, therefore, unlikely to cause vibration when external forces or moments caused due, for example, to a reaction from road surface during a steering operation act on opposite ends of the rack shaft.