Abstract A morphological search for molecular shells and cavities was performed around 63 Galactic supernova remnants (SNRs) at 10° ≤ l ≤ 50°, ∣b∣ ≤ 1° using the FOREST Unbiased Galactic Imaging survey with the Nobeyama 45 m telescope CO-line data at high-angular (20″) and high-velocity (1.3 km s⁻¹) resolutions. The results are presented as supplementary data for general purpose investigations of the interaction between SNRs and interstellar matter in the form of an atlas of CO-line maps superposed on radio continuum maps at 20 cm along with a list of their kinematic distances determined from CO-line radial velocities.