For trapezoidal canals in open water transfer systems, a novel method for calculating the distribution of non-linear normal frost-heaving force was proposed considering the horizontal difference of distance to groundwater table of each test point. Then Winkler assumption of the tangential force on the interface of frozen soil and lining was introduced to derive a calculation method of the distribution of non-linear tangential ad-freezing force. Eventually, a frost-heaving mechanical model of trapezoidal canal considering non-linear distribution of normal/tangential stress on the interface was constructed. Taking a trapezoidal canal in Tarim Irrigated Area as an example, the influence of groundwater table buried depth w on the distribution of section moment of concrete lining was analyzed by this model. The results show that the smaller the w is, the more non-linearly and rapidly the maximum value of section moment increases with heterogeneous distribution; sections of slope plate which are vulnerable to frost-heaving damage are located at the positions of 30%-42% slope plate length away from the slope toe, and those of the bottom plate are in the periphery of the bottom center, these findings are consistent with the field investigation results. A parameter analysis was carried out on the tangential displacement of each section and tangential ad-freezing force with different tangential stiffness coefficient of contact interface kp. The results indicate that the magnitude of both tangential displacement and tangential ad-freezing force gradually increase from the slope top to toe, which is zero on the slope top and maximum on the slope toe. when kp is small, both the tangential displacement and tangential ad-freezing force show the tendency of linear distribution; as kp gradually increases, both of them gradually deviate from linear distribution, and the larger the kp, the more non-linear the distribution. The study can provide references for frost-heaving resistance design of trapezoidal canals in cold regions.