Based on the general mathematical model of the clamping force of the belt conveyor in lifting section, the improved model to avoid the material leakage caused by the lateral movement of the belt was deduced. Based on the Hertz contact theorem, the mathematical model of elastic bulk material thickness in vertical lifting section, the relationship between the squeeze forces obtained by the material of outermost layer and the center (centroid) was deduced. The model was tried to apply in design of wheat transport machine, and was validated by the calculation. The model makes a partial improvement on the existing empirical formula of the clamping belt conveyor and the accuracy of the calculation, which provided theoretical support for the design, research and optimization of the specific parts of the belt machine, as well as other similar clamping conveyors.