A new generalization of the interface-current method for coupling two-dimensional heterogeneous assemblies, called substructures, has been developed. The method has been designed for fine-structure burnup calculations in large, very heterogeneous media. For the calculations, the medium is divided into rectangular substructures, which can have internal symmetries, containing rectangular and/or cylindrical structure elements, divided into homogeneous zones. A zonewise flat or linear expansion is used to formulate a direct collision-probability problem within each substructure. The substructures are coupled by making a piecewise uniform or linear expansion for the partial currents entering and leaving the substructures. The method has also been used to implement an approximate piecewise isotropic reflection for two-dimensional x-y collision probabilities calculations. The accuracies and computing times achieved are illustrated by one-group fixed-source numerical calculations for a typical 7 × 7 pin pressurized water reactor assembly as well as for a set of fuel slabs imbedded in a water moderator.