In this work, a computational chemical study of Etoricoxib was carried out at the B3LYP/6311G(d,p) level of theory, at the gas, aqueous and ethanol phases. Through the chemical reactivity descriptors derived from the DFT, it was possible to find that Etoricoxib structure exhibits a major chemical activity in water and ethanol phases in comparison to the gas phase, which suggests this drug would be more active in biological solvents like in blood, tissues and places where the ciclooxigenasa 2 (COX)-2 is found. In addition, a molecular docking analysis was conducted to study the interaction of Etoricoxib with the COX-2 active site. The results suggest that Etoricoxib interacts with 19 amino acid residues inside the COX-2 active site.