The independently developed and verified computational system BGUCORE for the neutronic analysis of pressurized water reactor cores is introduced. The basic methodology adopted generates cross-section libraries for each fuel type as functions of burnup and soluble boron concentrations. These cross sections are arranged as a two-dimensional matrix of sets, each set corresponding to a particular burnup/boron pair of coordinates. The two-dimensional diffusion analysis of the reactor core utilizes the pregenerated libraries by interpolating between burnup and boron entry points. The present system is especially designed for the analysis of cores with burnable poisons. Such cores are characterized by strong heterogeneity and selfshielding effects. Detailed benchmark calculations, performed for cycle 1 of the Zion 2 power station, validate the performance of the BGUCORE system. Further development of the system, aimed at creating a comprehensive design and fuel cycle analysis tool, includes a three-dimensional representation of the core and thermohydraulic modules.