Improvements in transmission and distribution networks can be noticed in most countries that had their system architecture changed by the deregulation process. In this new environment one of the biggest challenges is the transmission and distribution open access. In Brazil, the National Electricity Regulatory Agency has established that the monthly amount of transmission system usage contracted by a distribution company (DISCO) should be informed per connection point (one value for each point) between transmission and distribution network. The usage of the transmission assets are represented by the power flowing from the transmission system to the DISCO network. This implies in monthly charges at each border transformer (which represents a connection point) that the DISCO must pay to honor the contracts. If the DISCO exceeds the contract values by certain percentage, monetary penalties are incurred. The penalty costs can lead the DISCO to a more conservatory behavior at the time that the usage contracts are settled. On the other hand if the DISCO expects a low trend of its demand it has the possibility to contract less and save money. Determining the optimum amount to contract is a stochastic optimization problem because of future load uncertainties. This paper provides model formulations for the Transmission System Usage Problem with a real case study.