Abstract: The primary function of the nuclear power plant containment structure is to provide external protection against impacts and internal protection against leaks. In order to effectively control cracks and ensure the sealing of the container， a large number of prestressed tendons were adopted in the structure. The containment structure is a cylindrical structure system consisting of a cylindrical body and an upper dome， which requires the prestressed tendons to be arranged in a circular curve along the structure. There are some defects in the finite element software used to solve the prestressing effect of the cylindrical structure， resulting in certain errors in the results. Based on the theory of shell mechanics， using an iterative differential method to solve the equilibrium equation can yield the accurate effect of the curved prestressed tendons. This algorithm can also consider the influence of the cylinder thickness and accurately calculate the stress at any position along the cylinder thickness direction， providing accurate solutions for the containment prestressing design. Furthermore， the algorithm reveals the distribution of prestressing effects within the cylinder， which can provide suggestions for prestressing construction.