In a previous paper we have investigated the molecular environment towards the eastern border of the SNR G18.8+0.3. Continuing with the study of the surroundings of this SNR, in this work we focus on its southern border, which in the radio continuum emission shows a very peculiar morphology with a corrugated corner and a very flattened southern flank. We observed two regions towards the south of SNR G18.8+0.3 using the Atacama Submillimeter Telescope Experiment (ASTE) in the 12CO J=3-2. One of these regions was also surveyed in 13CO and C18O J=3-2. The angular and spectral resolution of these observations were 22, and 0.11 km/s. We compared the CO emission to 20 cm radio continuum maps obtain as part of the Multi-Array Galactic Plane Imaging Survey (MAGPIS) and 870 um dust emission extracted from the APEX Telescope Large Area Survey of the Galaxy. We discovered a molecular feature with a good morphological correspondence with the SNRs southernmost corner. In particular, there are indentations in the radio continuum map that are complemented by protrusions in the molecular CO image, strongly suggesting that the SNR shock is interacting with a molecular cloud. Towards this region we found that the 12CO peak is not correlated with the observed 13CO peaks, which are likely related to a nearby hii~region. Regarding the most flattened border of SNR G18.8+0.3, where an interaction of the SNR with dense material was previously suggested, our 12CO J=3-2 map show no obvious indication that this is occurring.