A numerical analysis for extracting the tensile and compressive creep power law parameters from flexural test data is applied to an SiC fibre-reinforced hot-pressed Si3N4 composite. The evolution and steady-state conditions of the stress distribution during creep and the effect of neutral-plane migration on the creep behaviour are also analysed. Finally, the kinetics and mechanisms of high-temperature creep in the composite are discussed with respect to the results of the numerical analysis.