Continuous welded rail (CWR) track has great advantages of low-cost maintenance, environmental influence, and ride comfort. However, the CWR track is subjected to the longitudinal stresses in rails due to temperature influence as well the inhomogeneous stress accumulation due to train loadings. The stresses cause the accelerated track lateral irregularity accumulation that without timely maintenance can cause track buckling. The present paper present a method of the CWR track lateral stability estimation during its lifecycle using the track geometry monitoring information from the track measurement cars. The methods proposes a systematic approach of track stability evaluation based on multiple criteria of track stability evaluation. It takes into account the lateral resistance of the track, actual temperatures, and the lateral geometry condition of the track. The presented case study of a half-year track geometry monitoring and the track stability evaluation in a track curve shows the practical possibility of the recent detection of the track sections with low lateral stability and buckling prevention.