In R-matrix calculations of electron-molecule scattering, matrix elements of the Hamiltonian operator are required in the form of integrals confined to a sphere fl around the target system. Evaluation of these integrals is a computational bottleneck, especially for polyatomic molecules. In this article we introduce a method in which integrals over ft are replaced by integrals over the entire coordinate space. This technique allows the use of standard integral programs, developed for bound-stale molecular calculations, which are of high efficiency. Such integrals are modified in a subsequent step by subtracting their contribution outside ft. Hereby we take advantage of a basic assumption, in R-matrix theory, that the potential outside of ft can be approximated by multipole potentials due to specified electronic target states. The applicability of the method is demonstrated and discussed for the resonant scattering process related to the metastable 2rr„ state of Nj. These calculations are restricted to fixed-nuclei electron scattering. © 1991 IOP Publishing Ltd.