An analytical model for calculating gas flow and pressure inside a nuclear fuel rod is presented. Such a model is required to calculate the pressure loading of cladding during ballooning that could occur for postulated reactor accidents. The mathematical model uses a porous media (permeability) concept to define the resistance to gas flow along the fuel rod. Permeability is expressed in terms of the diametral gap between the fuel pellet and cladding. The mathematical equations are solved numerically by means of a fully implicit finite difference procedure believed to be new to fuel rod gas flow analysis. The solution is direct, fast, and does not require iteration. The analytical model was found to agree quite well with experimental results for transient gas flow in irradiated fuel rods.