A model of the generation and release of fission gas, as well as the total swelling over time, was created. It uses an ideal spherical fuel grain with a time-dependent radius. UO2 and quasi-homogeneous SBR MOX fuels were simulated with this model, and the results were compared to a fixed grain radius model of gaseous swelling. Gaseous swelling and fission gas release were calculated for temperatures from 1600 K to 2200 K. The grain growth of UO2 was found to decrease the time needed to saturate the intergranular boundaries as compared to simple diffusion without grain growth. Small temperatures increased the time required for saturation, as did small rates of grain growth. Gaseous swelling was within the range of values found by experimental data.