For the English full text of the article please see the attached PDF-File (English version follows Russian version).ABSTRACT The data presented in the article testify to the urgent need for modernization of methods for studying horizontal geometric irregularities that provide necessary accuracy in assessment of the rail gauge state. The method for measuring the trajectory of the lateral surface of the rail head in the horizontal plane is improved. The method of converting the bending arrows from the base chord to the absolute values of the coordinates of the trajectory of the lateral surface of the rail head in the plan is modified. The influence of lateral wear of rails on traffic safety is evaluated. Particularly, the authors argue that along with the spectral methods of estimating the horizontal irregularities, it is necessary to apply the indicator of the traffic safety factor of single irregularities. According to the research the lateral undercut of the rail head in the longitudinal direction has an uneven wavy character and the results of its measurements should be used in assessing traffic safety, especially in curved sections of the track. Keywords: railway, track measuring car, horizontal irregularity, rail gauge, side wear of rails, traffic safety.