Numerical simulations of the flow of a vibrationally nonequilibrium gas around a circular cylinder have been undertaken. Distributions of velocity, temperature, and pressure in the wake behind the cylinder have been obtained, and the velocity fluctuation spectrum, which is measured in the experiment, has been examined. Three different models of medium and, accordingly, three different numerical schemes have been used. Comparison of the results enables one to identify the most important processes associated with the influence of relaxation, which result in some changes of the vortex street structure in comparison with the equilibrium case. Besides, such an approach enables one to verify the validity of the simplified methods used in numerical simulation of similar problems. Different conditions of heterogeneous relaxation on the surface of a cylinder are considered, and some comparison with experimental data is made.