One disadvantage of continuously welded rails is that the possibility of track buckling because of temperature increases is increased significantly by the elimination of rail joints. Many mathematical models have been developed for the buckling of tangent tracks, but there are very few that deal with curved tracks. The objective of this paper is the development of methods for the prediction of both the lateral thermal-buckling load and the corresponding displacement of curved tracks so that criteria for track design, maintenance, and evaluation can be formulated. This objective has been achieved by using a two-dimensional finite-element model that simulates the lateral stability of a track subjected to temperature increases and train wheel loads. This paper illustrates only the basic applications and the potential of the model. A parameter investigation was made that included tracks that had curvatures varying from 0 to 10 deg and studied the effects of various track parameters on the buckling temperature and the lateral track displacement. The results indicate that the buckling temperature and lateral displacement of a curved track are significantly affected by changes in lateral ballast resistance, misalignment and curvature, and by the presence of ineffective ties. The model provides a promising new approach to the track-buckling problem; however, test data are needed to validate it.