The Monte Carlo Adjoint Shielding (MASH) method has been developed to handle the case of a very complicated radiation shield that is irradiated from a distant source. It is not possible to accurately transport radiation to the vicinity of the shield and then through the shield to a dose point using Monte Carlo alone, even with bootstrap methods. Likewise, it is not possible to use discrete methods for the complete problem because of the shield geometry. The solution is to use a discrete method to transport radiation to the vicinity of the shield and then couple the incident radiation with an adjoint or importance Monte Carlo solution that starts all adjoint particles from the detector position. The methodology has been verified by experiment to give accuracies of 10 ? 20% for shielded vehicles 200 ? 1000 meters from a prompt fission source, and for vehicles situated on a large fallout field. The method has also been applied to a small concrete building and to a covered foxhole. Possible future applications are to large buildings in an urban environment, but more research has to be done to verify that the method is applicable to these problems.