A New method for calculating isolated resonance escape probabilities for slab lattices has been developed. It is based on the Boltzmann equation. The method avoids the use of Dancoff corrections and obviates the necessity of choosing between the wide and the narrow resonance approximations.The knowledge of the spatial dependence of the flux in the fuel region is not required. Isotropic scattering and a l/E spectrum above the resonance are assumed. The method is set up for a pure non-scattering uranium-238 absorber and a non-absorbing water moderator region. The reaction rate in the fuel region contains two contributions, the first term appears as an integral expression, which can be integrated numerically, the second term can be considered as a correction factor for oxygen scattering and is derived by using a variational approach. A computer code for calculating resonance escape probabilities in slab lattices has been developed. The results are in agreement with those obtained by Corngold. / Master of Science