The wheel–rail contact can be found in two patterns. In the first pattern, the treads of both wheels are in contact with the two top surfaces of the -shaped guide rail; in the second pattern, the treads of both wheels are in contact with the two top surfaces of the -shaped guide rail, and the wheel edge is in contact with the guide rail web on one side. Based on these findings, an equivalent mechanical model with four unilateral springs is proposed to describe the wheel–rail contact. Additionally, a dynamic model of the Translohr tramway is established using Matlab/Simulink. The wheel–rail contact in a tramway moving along curves with different radii is calculated using simulation, and the results obtained are consistent with the observations and results of field measurements. The effects of various factors, including curve radius, tram speed, guide rail pre-pressure, and guide rod length, on the side wear of the guide rail were investigated. The results revealed that curve radius and tram speed are the critical factors affecting rail track side wear. These two factors can qualitatively determine rail track side wear, while other factors can only quantitatively affect the degree of rail track side wear.