Damage to the surface of railway wheels and rails commonly occurs in most railways. If not detected, it can result in the rapid deterioration and possible failure of rolling stock and infrastructure components causing higher maintenance costs. This paper presents an investigation into the modelling and simulation of wheel-flat and rail surface defects. A simplified mathematical model was developed and a series of experiments were carried out on a roller rig. The time-frequency analysis is a useful tool for identifying the content of a signal in the frequency domain without losing information about its time domain characteristics. Because of this, it is widely used for dynamic system analysis and condition monitoring and has been used in this paper for the detection of wheel flats and rail surface defects. Three commonly used time-frequency analysis techniques: Short-Time Fourier Transform, Wigner-Ville transform and wavelet transform were investigated in this work.