Rail corrugation is characterised by bumpy railway tracks, causing undesirable noise and vibrations when trains pass over. The University of Queensland has developed a simplified numerical computer simulation model to analyse the problem in an attempt to identify the most critical parameters that affect the growth of the corrugations. The aim of this thesis was to develop analytical solutions in order to verify the results of the numerical model, and assist in understanding the fundamental mechanisms of rail corrugation formation and growth. These analytical solutions related to rail corrugation initiated by a flat and sinusoidal initial rail profile. The analytical solutions were compared with the numerical model in the time domain and good correlation was found for both the flat and sinusoidal initial profile cases. A growth rate analysis was also performed, and good results were achieved for the flat case, however the results for the sinusoidal case were unsatisfactory because of an unsuccessful frequency domain analysis.