The present study is aimed in providing a framework for applying different continuum models of relaxation processes in carbon dioxide flows. Kinetic equations for the distribution function are written taking into account the CO ₂ structure and various mechanisms of vibrational relaxation; collision operators for different internal energy transitions are derived. For weak non-equilibrium conditions, a one-temperature model is developed with emphasis to the bulk viscosity phenomenon. For strong non-equilibrium conditions, multi-temperature models are introduced, and their advantages and limitations are discussed. A general algorithm for calculating vibrational relaxation time in polyatomic molecules is proposed. Bulk viscosity coefficients are studied in the temperature range 200-2500 K; it is shown that uncoupling rotational and vibrational modes results in essentially overpredicted values of the bulk viscosity coefficient at low temperatures. The shock wave structure in CO ₂ is studied using the continuum models and compared with the solution obtained in the frame of the model kinetic approach; the effect of bulk viscosity on the shock wave width and temperature profile is evaluated. It is concluded that well justified choice of the model extends considerably the range of applicability of the continuum approach for non-equilibrium flow simulations.