The classical Navier‐Stokes theory was used to calculate profiles of plane shock waves in argon. The viscosity‐temperature relationship employed in the calculation was based on a Lennard‐Jones 6–12 intermolecular potential function for which the parameters were derived from experimental viscosity measurements up to 1100°K. With this viscosity function, the maximum‐slope shock thicknesses obtained were smaller than previously calculated assuming viscosity proportional toT0.816. Also it was found that the maximum‐slope thickness based on the density profile was less than that based on the velocity profile. The density profile thicknesses calculated with the Lennard‐Jones viscosity function were the same order of magnitude as, but not in quantitative agreement with experimental density thicknesses obtained with the optical reflectivity technique. It was found that Navier‐Stokes profiles become asymmetric as the shock strength is increased. However, the calculated asymmetry would have a negligible effect on thickness measurements by the optical reflectivity method.