Numerical simulations are presented of a steady-state, hypersonic e ow over a two-dimensional cylinder of 1 m radius under conditions where the relaxation of the vibrational modes is signie cant. A Mach 6.5 nitrogen e ow was simulated atfreestream pressuresof50, 250, and500 Pa, witha freestream translational temperatureof300K.Two differentfreestream vibrationaltemperatures,300K (causing vibrationalheating )and4000K(causing vibrational cooling)were considered to study the effects on the e owe eld. An upwind-difference numerical scheme was used to solve the inviscid Euler equations coupled to the vibrational kinetic models of diatomic nitrogen, assumed as an anharmonic oscillator of 40 quantum levels using two sets of reaction rates. Comparison with previously reported computations showed a maximum variation of 10% in translational and e rst-level vibrational temperature along thesurfaceduetodifferencesinnumericalschemesandgriddensities;variationcausedbythetwodifferentreaction rate sets was less than 2%. The vibrational cooling case showed a 10% higher shock-standoff distance than the vibrational heating case. The population distribution for the cooling case was non-Boltzmann due to nonresonant energy exchangesin the postshock region, greaterin theshoulder region than in thestagnation region. An increase in freestream pressure for the cooling case increased the shock-standoff distance and non-Boltzmann behavior in the postshock region and near the surface. There was, however, a larger equilibrium region in between, in the stagnation region.