A rail fastener includes a rail plate, a pad of elastomeric material between the plate and a support structure, and a pair of posts for laterally and longitudinally restraining the rail plate with an insulator bushing mounted between the posts and cooperating peripheral surfaces of the openings in the rail plate. Each of these posts is preferably formed of two parts, one of which is embedded in the support structure, and the other of which is an eccentric which is releaseably attached thereto. Rotation of the eccentrics provides lateral and longitudinal adjustment of the rail plate with respect to the support structures, thereby providing lateral adjustment of the rail with respect to the support structure.