Ocean currents are an attractive source of clean energy due to their inherent reliability, persistence and sustainability. The Gulf Stream system, particularly the Florida Current, is of interest as a potential energy resource for some coastal states within the USA. However, little is known about the potential impacts of extracting energy from this unconfined flow field. The presented study takes two approaches to evaluate the modifications of the flow field upon extraction of significant energy from the Florida Current. First, the theoretical momentum balance in the Gulf Stream system is examined using the two-dimensional ocean circulation equations based on the assumptions of the Stommel model for subtropical gyres with additional turbine drag formulated and incorporated into the model to represent power extraction by turbines. The impact of the extraction is evaluated by examining the new circulation patterns such as the flow diversion around the turbine extraction region. Secondly, a full numerical simulation of the ocean circulation in the Atlantic Ocean is performed using Hybrid Coordinate Ocean Model (HYCOM) and power extraction from the Florida Current is modeled as additional momentum sink. Various scenarios with different turbine distributions are tested. Effects of power extraction are shown to include flow rerouting from the Florida Strait channel to the east side of the Bahamas. Other effects, such as changes to the residual kinetic energy as well as the water level variations are also evaluated for different scenarios.