An important radiation transport problem is that of determining the effect of a geometrically complex object (vehicle) located in an otherwise geometrically simple system. The direct solution to this problem often requires a Monte Carlo calculation. If the vehicle is far removed from the radiation source, the calculation can be very costly or even impossible.To deal with this problem, a new method, the adjoint difference method, has been developed. This method decomposes the original problem into two independent calculations: 1. a geometrically simple (one- or two-dimensional) deep-penetration calculation that is independent of the vehicle 2. a localized three-dimensional calculation that is independent of the radiation source. The first calculation is suitable to deterministic methods of solution, such as discrete ordinates. The second, by nature of geometry, usually requires a Monte Carlo calculation; however, this is not a deep-penetration calculation. Therefore the dual complexity of geometry and statistics inherent in a deep-penetration Monte Carlo calculation is avoided. Since the above calculations are independent, only the coupling of these calculations depends on the relative position and orientation of the source and vehicle. Hence the effects of different sources and arbitrary vehicle orientations can be obtained from a single Monte Carlo calculation. The method was examined through application to several problems. All resuits were compared to those obtained from presently acceptable methods of problem solution. In these applications, the adjoint difference method was shown to be an efficient, versatile method of calculation.