A new particle transport theory method has been developed for application in particle streaming and shielding calculations. The method is similar to the SN technique in that discrete directions are used, and the transport medium is divided into spatial mesh cells. However, in addition to the spatial mesh, the entire medium is overlaid with a series of streaming rays. Particles are assumed to travel along these rays until they suffer collisions. The collided fluxes within and at the cell surface are related using a difference approximation technique. The collided particles are then reassigned to streaming rays. Unlike the SN method, differencing approximation schemes are required only for particles that have collided in the cell of interest. Another feature of this method is that a finer angular quadrature set is used for the streaming portion of the transport calculation than is used in the determination of the scattering source. The remaining aspects of the technique parallel those of the SN method. Several test results demonstrating the capability of the method are presented.