It is generally accepted that track support stiffness is a major factor controlling rates of track geometry deterioration, particularly where the track support stiffness changes abruptly. There is, therefore, considerable potential benefit in being able to quantify and detect changes in the track support stiffness. In recent years, trackside techniques using various types of transducer have been developed to determine track deflections as trains pass. However, deducing the track support stiffness from these measurements requires assumptions to be made concerning train loading and track behaviour, and scope for different interpretations remains. For example, loads from moving trains vary dynamically and it is not usually feasible to measure their exact values at any given point along the track. This paper presents new methods of analysis, which can be applied to frequency spectra of track displacement, velocity or acceleration generated as trains pass to calculate the track support stiffness for trains of known axle intervals, without needing to know the actual loads applied. The approach is demonstrated with reference to theory and measured data from a range of field sites.