Fischer-Tropsch synthesis is an important chemical process for the production of liquid fuels and olefins. In recent years, the abundant availability of natural gas and the increasing demand for olefins, diesel, and waxes have led to a high level of interest to further develop this process. A mathematical model of a slurry reactor used for syngas polymerization was developed, and carbon monoxide polymerization was studied from a modeling point of view. Simulation results show that different parameters affect syngas conversion and carbon product distribution, such as temperature, operating pressure, catalyst holdup, and syngas composition. Optimization of several hydrocarbon products were done in order to search for the best operating conditions for their production.