The strain rates, strains, and stresses resulting from irradiation growth and swelling in long cylindrical solid fuel elements in unsteady-state conditions are determined analytically. From the simple diffusion equation for nonequilibrium reactor system, an exact solution for neutron flux distribution is expressed by products of Bess el function with exponential time function. From the heat conduction equation with an internal heat source in unsteady state, a solution for temperature distribution in the fuel elements is obtained. A physico-mechanical analysis for the fuel elements is carried out with some basic assumptions concerning the properties, fabrication, end and yield conditions of the fuel, and cladding materials., The figures show the combined effects of radiation growth, swelling, and time on the components of the strain rate, strain, and stress produced in the fuel elements during reactor operation. The results are based on the derived equations and the calculated results of a numerical example.