Coupling neutronics to thermomechanics is important for the analysis of fast burst reactors because the criticality and safety study of fast burst reactors depends on the thermomechanical behavior of fuel materials. For instance, the shutdown mechanism or the transition between supercritical and subcritical states is driven by the fuel material expansion or contraction. The material expansion is due to the temperature gradient that results from fission power. In this paper, we introduce a numerical model for coupling of neutron diffusion and thermomechanics in fast burst reactors. The goal is to have a better understanding of the relation between the reactivity insertion and the thermomechanical response of fuel materials. We perform a nondimensional analysis of the coupled system that provides insight into the behavior of the transient. We also provide a semianalytical solution model to the coupled system for partial verification of our numerical solutions. We studied material behavior corresponding to different levels of reactivity insertion.