AbstractA longitudinal continuous structure will become vertically unstable under longitudinal temperature pressure. The classical analytical calculation method of this issue was insufficient to explain the rationality of the rigid foundation assumption and not accurate enough. Based on this, this paper did the following work. The stress and vertical deformation characteristics of a longitudinally continuous structure under longitudinal temperature pressure with a flexible foundation were analyzed. Based on the waveform curve after upper arch, the equilibrium path of vertical instability of the longitudinal continuous structure with initial irregularity was derived by the principle of stationary potential energy. An improved calculation method for vertical thermal instability in longitudinal continuous structure was also proposed, which was verified through a comparative analysis using experimental data and a finite-element calculation. Our proposed method was also compared with Taylor’s method. The results justify the assumption of a rigid foundation to approximate a foundation of finite stiffness (e.g., for longitudinal continuous track) in a mechanical analysis. The equilibrium path of longitudinal continuous structure under longitudinal temperature pressure involves three main stages: stability, expansion, and instability. Without considering the postbuckling, the friction coefficient affects the stability of longitudinally continuous structures negligibly. The equilibrium paths and the waveforms obtained by our proposed method, the test, and the finite-element calculation were relatively close, which validates our proposed method. The equilibrium path obtained by Taylor’s method changes in a manner similar to that obtained by our proposed method, but Taylor’s temperature rise is 24%–30% lower than that obtained by our proposed method (only considering the stability and expansion stage). It is concluded that the present method is more accurate.