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Introduction: The emergence of a new and highly pathogenic coronavirus (SARS-CoV-2) in Wuhan (China) and its spread worldwide has resulted in enormous social and economic losses. Amongst many proteins encoded by the SARS-CoV-2 genome, the main protease (Mpro) or chymotrypsin-like cysteine protease (3CLpro) and papain-like protease (PLpro) serve as attractive drug targets. Material and methods: We screened a library of 2267 natural compounds against Mpro and PLpro using high throughput virtual screening (HTVS). Fifty top-scoring compounds against each protein in HTVS were further evaluated by standard-precision (SP) docking. Compounds with SP docking energy of ≤ -8.0 kcal/mol against Mpro and ≤ -5.0 kcal/mol against PLpro were subjected to extra-precision (XP) docking. Finally, six compounds against each target proteins were identified and subjected to Prime/MM-GBSA free energy calculations. Compounds with the lowest Prime/MM-GBSA energy were subjected to molecular dynamics simulation to evaluate the stability of protein-ligand complexes. Results: Proanthocyanidin and rhapontin were identified as the most potent inhibitors of Mpro and PLpro, respectively. Analysis of protein-inhibitor interaction revealed that both protein-inhibitor complexes were stabilized by hydrogen bonding and hydrophobic interactions. Proanthocyanidin interacted with the catalytic residues (His41 and Cys145) of Mpro, while rhapontin contacted the active site residues (Trp106, His272, Asp286) of PLpro. The docking energies of proanthocyanidin and rhapontin towards their respective targets were -10.566 and -10.022 kcal/mol. Conclusions: This study's outcome may support application of proanthocyanidin and rhapontin as a scaffold to build more potent inhibitors with desirable drug-like properties. However, it requires further validation by in vitro and in vivo studies. [ABSTRACT FROM AUTHOR]