[en] Little effort has been made to develop numerical transport methods which can treat differential scattering cross sections which depend explicitly upon vector Ω' and vector Ω, where vector Ω' and vector Ω denote the incident and emergent particle directions, respectively. Such cross sections are called asymmetric. As a first step in the development of a general technique a finite-element collocation method was developed for the solution of the one-dimensional transport equation in slab geometry with asymmetric scattering. One of the unexpected results is that the reflection coefficient can be less than unity for particles incident upon a non-absorptive semi-infinite slab. A set of calculations using both the new technique and a standard Monte Carlo technique were performed for a 100-mean-free-path-thick slab. The diffusion values and the discrete-ordinates values are in excellent agreement with the Monte Carlo values. It is concluded that the discrete-ordinates method is a valid one with potential application to the transport of neutral atoms in anisotropic plasmas. 1 table