Diatomic and polyatomic molecules are characterized with additional degrees of freedom that may not be in equilibrium with each other in non-equilibrium flows. The assumption of common temperature for all modes may not be justified as the degree of non-equilibrium increases. In this study, we consider multi-temperature approach with NSF formulation to model rotational non-equilibrium in shock structures at high Mach number flows in diatomic gases. Parker’s model for rotational relaxation has been employed to model energy exchange between translational and rotational modes. Vibrational energy has not been considered for simplicity. Common gases such as \({\text {N}}_2\) , \({\text {O}}_2\) , and \({\text {Cl}}_2\) have been chosen to study the effect of gas properties on relaxation phenomena. It has been found that shock structures in \({\text {N}}_2\) and \({\text {O}}_2\) are similar while that in \({\text {Cl}}_2\) differs considerably. Besides, the effect of variable and constant rotational collisional numbers, viscosity models, and Mach numbers have also been carried out. Simplified models for viscosity variation with temperature such as power law model have been used to make the study simple but intuitive.