The computer code MARFA (Migration Analysis for Radionuclides in the FAr field) uses an extremely efficient particle-based Monte Carlo method to simulate the transport of radionuclides in fractured rock systems. The algorithm uses non-interacting particles to represent packets of radionuclide mass. These particles are moved through the system according to rules that mimic the underlying physical transport and retention processes. In contrast to the conventional random walk particle tracking algorithm, which use a specified time step and random spatial displacement, the MARFA algorithms use a fixed spatial displacement and a random transit time for the displacement. The use of a fixed spatial displacement makes the code extremely robust and computationally efficient.