The main objective of this research work is to develop a multiple perturbation Monte Carlo technique for nuclear reactor criticality problems. Even though the eigenvalue (or the multiplication factor) of the neutron transport equation can be estimated very efficiently by Monte Carlo methods, the calculation of small reactivity effects due to realistic cross section perturbations is much more difficult. For small perturbations, a direct correlated simulation is necessary instead of taking the difference between the results of two independent Monte Carlo simulations. The ability to calculate multiple eigenvalue perturbations from a single Monte Carlo simulation is extremely useful. Since Monte Carlo methods are computationally slow, this capability gives rise to an efficient Monte Carlo perturbation technique. There are quite a few cases in computational reactor physics for which it is desired to know the perturbations in eigenvalue due to cross section changes. These include calculations of perturbed eigenvalues due to different soluble boron concentrations, different number of absorber control rods in assemblies, and different assembly loading patterns for a global core, for example.