Abstract: Spent fuel reprocessing is a key step toward sustainable nuclear energy, and the Purex process which is a liquid to liquid extraction technique, has become the mainstream technology for the efficient and scalable recovery of uranium, plutonium, and other fission materials. The shearing-dissolution unit is the first chemical operation in the Purex process, responsible for converting fuel assemblies from solid to liquid, which has a significant impact on the safety and efficiency of subsequent separation and extraction steps. The batch dissolver is a typical reactor used at the front end of spent fuel reprocessing, and it controls the dissolution reaction process indirectly through intermittent feeding. However, due to the highly dynamic and multi-parameter coupled nature of the system, current mathematical modeling and dynamic simulation studies on batch dissolver systems remain relatively scarce, restricting process optimization and scale-up engineering. Based on the principle of mass conservation, in this work a coupled shearing-dissolution mathematical model for batch dissolvers was established, and key processes including fuel shearing, particle volume reduction, dissolution reaction kinetics, and mass transfer were systematically described. The model introduces cylindrical geometry and a surface area correction factor, incorporates sub-boiling dissolution and batch feeding operation, and is implemented using a Python-based numerical simulation platform. Under typical process conditions (uranium dioxide mass of 523.4 kg, temperature of 95 ℃, initial nitric acid concentration of 6.1 mol/L, and surface area correction factor of 1), the simulation shows that the system reaches the discharge criterion at 234 min and achieves compositional equilibrium at approximately 800 min. At equilibrium, the uranium ion concentration is 318.81 g/L, nitric acid concentration is 1.41 mol/L, and the dissolution rate of uranium dioxide reaches 99.15%. The model’s simulation of solute concentration evolution under typical conditions closely matches theoretical data, with a relative mass balance error of only 0.007 2%, thus verifying the accuracy and stability of the modeling and algorithm. Furthermore, parametric studies of varying shearing intervals, dissolver liquid volume, initial nitric acid concentration, and surface area correction factor provide deeper insight into the effects of key operating parameters on the dissolution process dynamics. A local sensitivity analysis using the finite difference method was conducted to investigate the parameter sensitivity of uranium ion concentration with respect to initial nitric acid concentration and surface area correction factor. The proposed model effectively characterizes the dynamic behavior of batch dissolvers and demonstrates good engineering applicability and generalizability, providing reliable theoretical and data support for the optimization and design of spent fuel reprocessing processes.