Abstract: Trapezoid canal with arc-bottom is widely used in cold and aridity areas in northern China because of its better capacity of resisting frost-heaving damage and hydraulic characteristic. However, there have not been any accurate mechanics calculation model about this kind of lining structure, the design of this lining structure depends only on the experience, and it can not make quantitative design and calculation. Through the analysis on the damage mechanism and damage characteristic of the frost-heaving of the concrete lining of trapezoidal canal with arc-bottom, the entire structure can be regard as thin-shell arc structure under the loads of normal frost-heaving force, tangential freezing force and gravity, and this belongs to the problem with both bending and compressing deformation. Using rational hypothesis and simplification, a mechanics models was proposed to analyze the frost-heaving damage of the entire structure with concrete lining, the formula was acquired to calculate the internal forces controlling frost-heaving and the maximal tensile stresses. By considering the conditions of resisting the crack of concrete plates, the calculation methods for analyzing the position of expansion cracks，the proper depth of the lining plates preventing the occurrence of frost-heaving and cracks , and the checking calculation on resisting frost-heaving were proposed. The theory analysis indicate that the concrete lining structure of trapezoid canal with arc-bottom, the normal frost-heaving force is small and uniform, the resilience is large, so it has stronger capability of adapting entire deformation and resisting frost-heaving, and it is better than trapezoid canal. The results of examples show that the mechanics model is safety, rationality, briefness and practicability.