A new method is developed to determine space-dependent, self-shielded cross sections for resonance nuclides with no overlapping resonances, contained in an arbitrarily shaped absorber body within some general lattice configuration. The theoretical basis for the method is discussed, and analytical expressions are presented for the space-dependent flux spectrum in the vicinity of an isolated resonance and for the space-dependent variation in the shielded resonance integral and multigroup cross section. The shielded cross-section expressions contain space-dependent, “weighted escape probabilities” that correspond to the weighted average of the energy-dependent escape probability over each energy group. The method is implemented in an assembly lattice physics code, and results are compared to those obtained with a highly accurate transport theory calculation that uses pointwise cross-section data. The method gives good agreement for the radial variation in the self-shielded cross section through a boiling water reactor fuel pellet.