Abstract: Once fuel element was failed, the fission products would be released into the primary coolant, leading to the increasing of radioactivity level of the primary coolant. According to the monitoring data of fuel element failure, using a certain calculation method, the number of failed fuel elements was calculated, which can be provided the important basis for dealing with the accident of fuel element failure and ensuring the security of the reactor and staff. In this paper, the behaviors of the delayed neutron precursors, including its birth, releasing and migration, and the response of detector were studied, and the mathematical models for every process were built. Combined with these models, the method to calculate the number of failed fuel elements was formed, which can be applied to the calculation of the number of failed fuel elements for many type of reactors.