A two energy group model is proposed in this paper for studying the criticality of a slab of finite thickness in the framework of neutron transport theory. The system of the two stationary Boltzmann equations which, in the case of isotropic scattering, govern the flux distributions of the two neutron groups, is first solved by a Fourier transform technique. Explicit series expressions are then derived for the angular as well as for the total flux distributions in the interior and at the boundary of the critical slab. These series expressions are shown by numerical calculations to be rapidly convergent to the required solutions of the problem under examination. Results for the critical parameter and for the total and angular flux distributions are at last reported.