When a pressurized water reactor is operated for a sufficiently long period of time, a small number of fuel rods will develop ruptures in their claddings. These defects will leak volatile fission products into the primary coolant, including radioactive iodine. During steady-state operation of the reactor a low level iodine activity is thus present in the coolant. Initiation of a down-power or up-power transient will result in a rapid climb in the activity of the iodine which peaks at a level much higher than the initial activity. After this time the activity levels out and then slowly begins to decay back to a new steady-state level. This phenomenon is termed "iodine spiking.” A physical model of this process is sought for explanatory and predictive purposes. A FORTRAN code is developed that solves a system of differential equations which describe the production and removal of iodine in the fuel, gap region, and primary coolant. As much physics as possible is employed but some complicated diffusion processes have led to the utilization of certain parametric results obtained from empirical data. Actual PWR spiking data is also employed for comparison and adjustment of the model. It is the goal of this project to be able to utilize the model for predictive analysis· during actual PWR operation so that a better understanding of iodine spiking behavior can be obtained. / Master of Science