Abstract: The current fracture mechanics analysis approach for assessing frost-heaving damage in lined canals located in cold regions lacks the consideration of both the interaction between frozen soil and the lining structure and the influence of temperature-induced stress caused by thermal contraction of the lining. In light of this, the three-parameter Kerr model is utilized to elucidate the interaction between frozen soil and lining. The governing differential equations are systematically derived, and an analytical solution for the frost heave deformation of the lining plate was obtained by combining the undetermined exponential function method with the Cardano formula. The governing equation for tangential displacement induced by temperature variations is derived under the conditions of static equilibrium. This equation is subsequently solved to yield an analytical expression for thermal stress. A comprehensive fracture mechanics analysis method for trapezoidal canal linings is proposed, which accounts for both the bending deformation caused by soil frost heave and the effects of subzero temperatures in accordance with the principles of linear elastic fracture mechanics theory. Guidelines for identifying the most vulnerable sections and establishing frost-heaving fracture criteria for concrete lining are provided. Using a trapezoidal canal in the Tarim Irrigation District as an example, the article employs the traditional Winkler model, the finite difference method, and the presented approach to calculate the frost-heaving deformation of lining plates. The obtained results are then compared with observed values to validate the rationality and applicability of the model proposed. The parametric analysis indicates that the stress intensity factors of each lining section exhibit varying degrees of augmentation in response to the increase in natural frost heave amount, of the absolute temperature difference, and of the initial crack length. Neglecting the subzero temperature effects will lead to an underestimation of the stress intensity factor in the most vulnerable sections, thereby introducing a bias toward unsafe conditions in the calculation results. Cracks situated in the lower middle section of the lining plate are more prone to unstable propagation, which can ultimately result in structural failure. This finding is consistent with the results obtained from the on-site investigations conducted within the irrigation area. These study results will serve as a valuable reference for anti-crack calculations related to concrete lining structures in canals in cold regions.