Abstract The shell-type supernova remnant HESS J1731 − 347 emits TeV gamma-rays, and is a key object for the study of the cosmic ray acceleration potential of supernova remnants. We use 0.5–1 arcmin Mopra CO/CS(1–0) data in conjunction with H i data to calculate column densities towards the HESS J1731 − 347 region. We trace gas within at least four Galactic arms, typically tracing total (atomic+molecular) line-of-sight H column densities of 2–3× 1022 cm−2. Assuming standard X-factor values and that most of the H i/CO emission seen towards HESS J1731 − 347 is on the near-side of the Galaxy, X-ray absorption column densities are consistent with H i+CO-derived column densities foreground to, but not beyond, the Scutum–Crux Galactic arm, suggesting a kinematic distance of ∼3.2 kpc for HESS J1731 − 347. At this kinematic distance, we also find dense, infrared-dark gas traced by CS(1–0) emission coincident with the north of HESS J1731 − 347, the nearby H ii region G353.43−0.37 and the nearby unidentified gamma-ray source HESS J1729 − 345. This dense gas lends weight to the idea that HESS J1729 − 345 and HESS J1731 − 347 are connected, perhaps via escaping cosmic-rays.