The use of the method of discrete ordinates as a numerical tool in reactor calculations is described. A scheme for the numerical integration of the discrete ordinate equations is developed, and the results compared with known exact solutions. The problem of reflection and transmission of neutron beams in stratified slab geometry is considered from the point of view of the method of discrete ordinates. A matrix formalism is derived which permits the calculation of transmitted and reflected distributions if the incident beam is given. Asymptotic expressions for the relevant matrices are given, and comparison is made with the work of Chandrasekhar. Tables of the matrix elements in the P7 approximation are presented.