The thermal ratcheting deformation at the reactor baffle and upper internal structure of the liquid metal reactor (LMR) can occur due to movement of the hot sodium free surface. In in-service inspection of reactor internals of LMR, a new inspection technique should be developed for the detection of the thermal ratcheting damage. In this study, an inspection technique using ultrasonic guided wave is proposed for the detection of the thermal ratcheting damage of cylindrical vessels. A 316L stainless steel cylindrical shell specimen has been prepared. The thermal ratchet structural tests were cyclically performed by heat-up up to $550^{circ}C$ with steep temperature gradients along the axial direction after cool-down by cooling water. Ultrasonic guided wave propagation has been characterized by analysis of dispersion curve of the stainless steel plate. The zero-order antisymmetric $A_0$ guided wave has been selected as the optimal mode for detection of the ratcheting deformation. It is confirmed that the thermal ratcheting deformation can be detected by the measurement of transit time difference of circumferentially propagated $A_0$ guided waves.