Abstract: During use, a wheel of a railway vehicle may become out of round, which will be detrimental to both the vehicle suspension and the railway track. The shape of such a wheel may be monitored to detect any such out of roundness, while the wheel is rolling, by measuring how far the flange of the wheel projects below the upper surface of the rail. This may be achieved by mounting a rigid bar (24) alongside the rail (10), the bar (24) being supported resiliently so as to be depressed by a flange of a wheel (40), and by measuring the vertical displacement of the bar. The bar (24) may be supported by a plurality of flat leaf springs (26), which are inclined to the horizontal at for example 30°. This ensures that the bar (24) remains substantially parallel to the top surface of the rail (10) when depressed by the flange of a wheel (40).