Large dynamic stresses are induced in the fuel components of fast-burst, or pulse, reactors because of rapid fission heating. These stresses increase more than linearly with burst energy yield and, at some yield, will cause fuel failure. Despite many attempts, no one has yet succeeded in predicting a fuel damage threshold with useful certainty in the reactor design stage, nor has the maximum fuel stress for a given power pulse in an operating reactor been calculated satisfactorily. Some analytic solutions for the burst dynamic behavior of typical fuel components that are consistent with available fuel displacement measurements are discussed. In particular, an analytic function is introduced for stress-vibration excitation of fuel components by the bell-shaped power pulse of a reactor burst. These solutions can be employed to determine fuel damage thresholds with useful certainty. Also, a new approach is presented for the analysis of prompt burst power transients by employing fuel displacement solutions to derive dynamic reactivity quench for use in power calculations.