Certain analytical elastic solution for curvilinear track section under uniform thermal loading has been proposed. Track section is composed of circular arc, transition curves and straight lines. Next step is the analysis of two-dimensional model of the track structure (stress plane, without vertical direction). The rails and the sleepers are assumed as elastic bodies. The fasteners and ballast are modeled as elastic-plastic elements. Non-linear properties of these elements are determined by comparison of numerical data with experimental results. Cyclic uniform thermal field is applied as the load of the system. Pre-buckling analysis is the basic part of the considerations. Certain remarks on the track stability, based on the previous author analyses, are also presented. It is shown that track structure with Y-shaped steel sleepers gives the possibility to use of continuous welded rail (CWR) track practically in any radius of curvature.