The SARS-CoV-2 main protease (Mpro) plays an important role in the viral transcription and replication of the SARS-CoV-2 virus that is causing the Covid-19 pandemic worldwide. Therefore, it represents a very attractive target for drug development for treatment of this disease. It is a cysteine protease because it has in the active site the catalytic dyad composed of cysteine (C145) and histidine (H41). The catalytic site represents the binding site for inhibitors, many of them bind to Mpro with a covalent bond. In this research, structural and physiochemical characteristics of the Mpro binding site are investigated when the ligand 11a is covalently and non-covalently bound. All-atom molecular dynamics (MD) simulations were run for 500 ns at physiological temperature (310 K). It is found that conformations of both the Mpro protein and the ligand are stable during the simulation with covalently bound complex showing stronger stability. When the ligand is covalently bound (its final state), residues that stably interact with the ligand are H41, C145, H163, H164 and E166. The optimal conformation of these residues is stabilized also via the Hbond interactions with the catalytic water present in the Mpro binding site. In the case of the non-covalently bound ligand (state before the covalent bond is formed), the binding site residues retain their conformations similar to the covalent binding site, and they still form Hbonds with the catalytic water, except H41. This residue, instead, adopts a different conformation and looses the Hbond with the catalytic water, leaving more freedom to move to the ligand. We hypothesize that H41 could play a role in guiding the ligand to the optimal position for final covalent bonding. Further analyses are in process to check this hypothesis. These results represent an important basis for studying drug candidates against SARS-CoV-2 by means of computer aided drug design.