Based on elasticity, an elastic model was used to derivate the stress function and the stress expressions. According to the stress boundary condition and the geometry dimension of a cylinder-cross-section pipe, the constants are determined. First supposed the pipe were empty and the inner pressure were zero, the maximum prestress for the reinforced concrete pipe was determinate. Second, supposed the liquid pressure was the maximum, the model was used to determinate the minimum prestress. Combined the two critical conditions, the reasonable range of prestress for reinforced concrete pipe was got. In designing, the prestress must be consistent with it to prevent the concrete from crushing or bursting. At last, some differences between the theory result and the fact were pointed out to guide the application of the model.