Candidates to being inhibitors of the main protease (Mpro) of SARS-CoV-2 were selected from the database of Voronezh State University using molecular modeling. The database contained approximately 19,000 compounds represented by more than 41,000 ligand conformers. These ligands were docked into Mpro using the SOL docking program. For one thousand ligands with best values of the SOL score, the protein–ligand binding enthalpy was calculated by the PM7 quantum-chemical method with the COSMO solvent model. Using the SOL score and the calculated protein–ligand binding enthalpies, eighteen compounds were selected for the experiments. Several of these inhibitors suppressed the replication of the coronavirus in cell culture, and we used the best three among them in the search for chemical analogs. Selection among analogs using the same procedure followed by experiments led to identification of seven inhibitors of the SARS-CoV-2 replication in cell culture with EC50 values at the micromolar level. The identified inhibitors belong to three chemical classes. The three inhibitors, 4,4-dimethyldithioquinoline derivatives, inhibit SARS-CoV-2 replication in Vero E6 cell culture just as effectively as the best published non-covalent inhibitors, and show low cytotoxicity. These results open up a possibility to develop antiviral drugs against the SARS-CoV-2 coronavirus.