Fast spectrum reactors are essential for the future of nuclear energy. Therefore, there is a need for continuous research and development of the design and safety of current and future nuclear fast reactors. The aim of this work is to analyze the process of fuel burnup in a large scale (3600 MWth) Sodium cooled Fast Reactor (SFR) core. This design is called European Sodium Fast Reactor (ESFR). It is proposed in the 7th Framework Programme within the Euratom Framework. A new version (version 2.7) of Monte Carlo neutron transport code (MCNPX) was used to design a 3D model of the ESFR core to evaluate and analyze a number of burnup-relevant characteristics. These include the flux and power distributions across the ESFR core as well as the reactivity changes and fuel transmutation during burnup to take into account the changes in fuel composition during burnup. Obtained results can serve as up to date evaluation for the design and well allow for a detailed assessments of the fuel performance inside the ESFR core.