The importance of the viscosity cross section for elastic electron-atom collisions in various domains of electron kinetic and transport theories is pointed out. Results of numerical evaluations of the velocity-dependent viscosity cross sections for elastic electron-atom collisions in argon and neon are presented and discussed. Two series of results are given. They are based on theoretical and experimental sets of partial-wave phaseshifts for the two atomic species, taken from the literature. Special consideration is given to deviations, sometimes very significant, of the results obtained in the present calculations from those which would have followed if the scattering were assumed isotropic.