The Monte Carlo method is a statistical method that attempts to simulate the behavior of large numbers of neutrons and other nuclear particles. This chapter shows how the Monte Carlo method can be used to solve important problems in nuclear science and engineering. The Monte Carlo method is applicable to an almost unlimited number of problems in particle diffusion and transport theory and is not limited to just neutron or photon behavior in reactor fuel assemblies. It can be used to solve radiation shielding problems, compose music, and even decide when to buy or sell stocks. The Monte Carlo method is best suited for modeling complex reactor geometries where other methods either fail to predict the behavior of the particle population correctly or are too expensive to use. A Monte Carlo simulation begins by designing a random number generator that implements what is known as a statistical probability distribution function.