Molecular modeling approaches are an indispensable part of the drug design process. They not only support the process of searching for new ligands of a given receptor, but they also play an important role in explaining particular activity pathways of a compound. In this study, a comprehensive molecular modeling protocol was developed to explain the observed activity profiles of selected µ opioid receptor agents: two G protein-biased µ opioid receptor agonists (PZM21 and SR-17018), unbiased morphine, and the β-arrestin-2-biased agonist, fentanyl. The study involved docking and molecular dynamics simulations carried out for three crystal structures of the target at a microsecond scale, followed by the statistical analysis of ligand–protein contacts. The interaction frequency between the modeled compounds and the subsequent residues of a protein during the simulation was also correlated with the output of in vitro and in vivo tests, resulting in the set of amino acids with the highest Pearson correlation coefficient values. Such indicated positions may serve as a guide for designing new G protein-biased ligands of the µ opioid receptor.