Eucalyptus is the main fast-growing tree for biomass production in the tropics, providing resources for pulp and paper industries and bioenergy. The potential productivity of forest sites over an eight-year rotation in Brazil was evaluated by the Physiological Principles in Predicting Growth (3-PG) model for two soils, Acrisols and Arenosols, with high and low water storage, respectively, and distinct productive potential capacity. The model was parameterized by data-sets obtained in bimonthly forest inventories performed in stands with 33, 58 and 89 months-old trees, and edaphic surveys. The average volumetric productivity of wood and biomass of the main stem determined at the 89 months-old stand was 374 m3 ha−1 (177 Mg ha−1) for Acrisols and 272.3 m3 ha−1 (130.0 Mg ha−1) for Arenosols. The estimated volumetric production in the Arenosols had a high mean annual increment up to the age of 58 months, with a significant reduction in growth rates after this time. In Acrisols, high incremental rates in wood volume up to age of 89 months (MAIVW > 50 m3 ha−1 year−1) indicate that, under ideal soil conditions, the cutting cycle may exceed 8 years with no productivity impairment. The parameterized model matched well for forest yield (r2 > 0.9) and dendrometric variables (r2 > 0.78). The expected results of lower productivity in Arenosols occurred only after 58 months, while for Acrisols productivity remained high up to 89 months. The results showed the eucalyptus cycle should be shorter in Arenosols, since the lower cutting cycle can provide higher final productivity, when using the mean annual increment to evaluate productivity.