Atomic simulations of shock waves in gases have been performed using both molecular dynamics and the direct simulation Monte Carlo method devised for the Boltzmann equation. The profiles of the fluid density, velocity and temperature computed across the shock are shown to agree with the Navier-Stokes description for weak shocks (Mach numbers ranging up to 2) but then on the discrepancy increases with the Mach number. The Burnett modification to the Navier-Stokes equations is compared to the simulation results .