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The supernova remnant HESS J1731-347 is a young supernova remnant (SNR) that displays a nonthermal X-ray and TeV shell structure. A molecular cloud at a distance of ∼3.2 kpc is spatially coincident with the western part of the SNR, and it was likely hit by the SNR. The X-ray emission from this part of the shell is much lower than from the rest of the SNR. Moreover, a compact GeV emission region coincident with the cloud has been detected with a soft spectrum. These observations seem to imply a shock-cloud collision scenario at this area, where the stalled shock can no longer accelerate super-TeV electrons or maintain strong magnetic turbulence downstream, while the GeV cosmic rays (CRs) are released through this stalled shock. To test this hypothesis, we have performed a detailed Fermi-LAT reanalysis of the HESS J1731-347 region with over nine years of data. Two distinct GeV components are found, one displaying a soft spectrum is from the compact GeV emission region, the other one displaying a hard spectrum is from the rest of the SNR (excluding the cloud region). A hadronic model involving a shock-cloud collision scenario is built to explain the γ-ray emission from this area. It consists of three CR sources: run-away super-TeV CRs that have escaped from the fast shock, leaked GeV CRs from the stalled shock, and the local CR sea. The X-ray and γ-ray emission of the SNR excluding the shock-cloud interaction region is explained in a one-zone leptonic model. Our shock-cloud collision model explains the GeV–TeV observations from the clouds around HESS J1731-347, i.e., a cloud in contact with the SNR and a distant cloud in spatial coincidence to the TeV source HESS J1729-345. We find however that the leaked GeV CRs from the shock-cloud collision do not necessarily dominate the GeV emission from the clouds, due to a comparable contribution from the local CR sea. [ABSTRACT FROM AUTHOR]