A new neutron transport method, called discrete elements (LN), is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation.The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The zeroth and first angular moments of the directional flux, over each element, are estimated by numerical quadrature and yield a flux-weighted average streaming direction for the element. Data for this estimation are fluxes infixed directions calculated as in SN. The spatial quadrature then propagates the element flux in this “steered” direction, strongly ameliorating ray effect. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the LN method is more consistently convergent toward a Monte Carlo benchmark solution.