A methodology for the accurate description of three dimensional track geometries is proposed. Cubic, Akima and shape preserving splines are proposed for track parameterisation. The track description uses Frenet frames that provide the track referential at every point. During dynamic analysis a pre-calculated database is linearly interpolated to form the kinematic constraints that enforce the wheelsets of the vehicle to move along the track with a prescribed angular orientation. This approach allows calculating the reaction forces that develop between the vehicle and the track. The formulation is discussed emphasizing the influence of the parameterisation methods to construct the track geometry.