The aim of this paper is to investigate the possibility of improving the ride quality of a two-axle railway vehicle with a single-stage suspension by means of passive suspensions employing an inerter device. The inerter is a mechanical one-port element that is analogous to a capacitor in electrical circuits. The goal is to improve the ride quality in both the vertical and lateral motions in response to track irregularities. Performance benefits for several simple passive suspension layouts are demonstrated and compared with the conventional scheme. The elastic effects of the damper and inerter device are then taken into consideration for practical purposes. The optimum parameter values of the damper, inerter and the parameters representing the elastic effects provide guidance for mechanical design purposes.