The problem of monoenergetic neutral particle transport in an evacuated duct of arbitrary cross-sectional geometry with partial isotropic reflection at the duct walls is considered. This five-variable (three in space, two in angle) transport problem is approximated by a coupled set of N two-variable (one in space, one in angle) problems via a simple Galerkin (or variational) procedure. Numerical comparisons with exact results indicate that the N = 2 approximation is remarkably accurate for predicting the wall absorption and particle fluxes at the duct ends.