The logistics system for soy beans in grains is an important element in its production chain, since most of the corresponding costs is a result of transportation and warehousing costs. In this way, the optimization of this segment is essential for the competitivity of the Brazilian soy beans in the international markets. In this dissertation, the proposal is to develop a spatial multimodal and intertemporal equilibrium model using non linear programming. The applicability of the model is tested in a case study about the exports of soy beans produced in the state of Tocantins in the north part of the Brazilian cerrado, whose competitivity is related to those of the neighboring states of Maranhão and Piauí, that have the same transportation corridors. Finally, some alternative scenarios are considered to analyse the competitivity of the focused State. The results show, in the four evaluated scenarios, that the logistics costs are reduced when the multimodality happens in a intertemporal environment. They also show that the inclusion of the Hidrovia Tocantins becomes the State of Tocantins competitive. The data are treated by the GAMS/MINOS program developed for non linear problems. It is hoped that the results might offer subsidies to the State of Tocantins in order to allow a better evaluation of its transportation and warehousing infrastructure investments.