In the KALIMER (Korea Advanced Liquid Metal Reactor) design, the reactor baffle structure is adopted to prevent the hot pool sodium from directly contacting the reactor vessel and to guide the hot sodium overflow in severe transient operating conditions. The parts in the vicinity of the hot pool free surface region could be repeatedly subjected to a moving axial temperature gradient and this might result in thermal ratcheting deformation. In this paper, the progressive thermal buckling behaviour following thermal ratcheting due to the moving axial temperature gradients in a cylindrical shell structure with an open free edge is investigated using numerical inelastic analysis with Chaboche's model. To do this, the analyses of the moving temperature distribution are carried out with a simple model and the severe moving axial temperature gradients are assumed to be sufficient for the evolution of thermal ratcheting.