The present paper deals with the effect of releasing the constraining assumption of using an infinitely rigid foundation in the analysis of vertical buckling of a railroad track due to constrained thermal expansion. The chosen foundation is of the Winkler type. The buckled configuration is assumed to consist of two regions, i.e., a lift-off region and an attached region. The foundation resistance to the longitudinal displacement of the track is assumed to be linear. The problem is treated as a variational problem with variable end points for which the variational formulation yields a consistent set of differential equations and boundary conditions. It is found that a decrease in the foundation stiffness will increase the "safe buckling temperature." However, for the working range of an actual foundation, this increase is small and the assumption of an infinitely rigid base can be used to predict a close lower bound for the "safe buckling temperature."