Abstract: Based on the nuclear reaction of ¹³⁷Cs and ¹³⁴Cs in the fuel assembly, the accurate mathematical and physical calculation models were established. The exact and simplified solutions of relationships between radioactivity of the two nuclides in the primary coolant and burn-up of ²³⁵U in the fuel assembly were obtained. The comparisons of simplified solution, ORIGEN2.0 calculation result and exact solution were carried out as well. The result showed that, if only the R_Cs, ratio of ¹³⁴Cs/¹³⁷Cs in the primary coolant, is obtained by hydrochemistry measurement, burn-up of the ruptured fuel assembly can be calculated with the analytical solution model, so as to locate the ruptured fuel assembly rapidly.