To perform fast-neutron penetration calculations, a new method is described, which offers some of the advantages of the Monte Carlo method and other highly sophisticated methods, yet retains some of the features of the line-of-sight kernel methods. The method includes the use of effective flux-removal cross sections to predict a distribution of ‘last-collision’ centers in a shield and uses statistical estimation to obtain the flux at the receiver from each last collision. The chief advantage of the method is that it provides an approximate angular distribution of the neutron flux at the receiver and includes the effects of boundaries, but is much less costly to apply than Monte Carlo. The principal limitation to the accuracy of the method stems from the assumption of no change in neutron direction and energy prior to the last collision. Detailed formulations for slab and for cylindrical geometries are given, along with results of an initial evaluation based on comparisons with Monte Carlo and with measured data for lithium hydride shields.