The subject of this thesis is the develoment of a C++ software solution for criticality simulations of fissile assemblies using the Monte Carlo method. The input file contains sufficient data to define the simulation model. The program warrants the development of a suitable formal grammar to describe the input file complete with lexical and syntax rules. To generate the input parser Lex and Yacc, more precisely, their respective GNU extentions were used; namely Flex and Bison. Flex takes an input file with regular definitions of the lexical tokens and generates a lexical analyzer in C++. Bison takes, as its input, a file containing the productions of the formal grammar as well as their corresponding semantic actions. Bison generates a syntax analyzer in C++. The model geometry is constructed by using combinatorial geometry (Boolean algebra) on a set of primitive shapes i.e. analytic surfaces to yield closed 3D shapes with finite volumes filled with materials (nuclear cross sections) of interest. Along with geometric definitions, the input file also contains several control parameters, such as the number of active and inactive cycles, the initial effective neutron multiplication factor eigenvalue (keff) and the initial spatial distribution of neutrons. The a priori defined number of inactive cycles does not go into the final statistical estimate of the multiplication factor, instead they are used for the sole purpose of achieving the source eigenmode. The NCDS (Nine Center Distances Sum) metric is used as the source convergence indicator. Only after the source eigenmode has been achieved does the program begin tracking the particle random walks, these cycles are known as the active cycles. When a fission event occurs the resulting neutrons are store in a dedicated data structure, the fission bank. The final program output is a statistical estimate of the effective neutron multiplitcation factor and its standard deviation. Three estimators are combined to yield the final keff value, based on: absorption, scattering and traversed path length.