Mexico City soil has very high specific surface, plasticity and void ratio; its natural structure is preserved until the yield pressure σ’y, which is typically above the in situ effective stress σ’v, and the mechanical response changes significantly when the effective confining stress σ’o exceeds the yield pressure σ’y. In this study, the effects of strain rate on the undrained response of Mexico City soil are explored using undisturbed specimens subjected to monotonic triaxial compression tests at a constant rate of deformation. Results show that strain-rate effects on undrained strength and mode of failure depend on σ’y / σ’o, hence, on the degree of natural structure preserved in the specimen. Undrained strength increase with strain rate, particularly in the more structured specimens i.e., higher σ’y / σ’o. The role of σ’y / σ’o on strain-rate effects in this unremolded natural soil resembles the effect of overconsolidation ratio on resedimented specimens. The limitations in using standard triaxial equipment for strain-rate effect studies are discussed.