A comparison is made between the continuum and kinetic approaches in studying the shock wave structure in argon, nitrogen, and carbon dioxide. Using the kinetic-theory methods, one-temperature and two-temperature fluid-dynamic equations are derived and closed. Calorically non-perfect gas model is applied, with vibrational energy explicitly calculated. The algorithm for the calculation of transport coefficients including bulk viscosity is implemented. For argon and nitrogen, a good agreement of the solutions obtained using both the continuum approach and direct statistical simulations (DSMC) with experimental results is shown. For carbon dioxide, the one-temperature Navier-Stokes equations do not reproduce non-monotonic temperature behaviour. The two-temperature model yields the results qualitatively similar to those given by DSMC; quantitative discrepancies are however significant. The DSMC relaxation rate strongly depends on the vibrational collision numbers in various CO2 modes.