The planar Couette flow for gaseous mixture He–Ar is calculated by the direct simulation Monte Carlo method based on ab initio potential over the whole range of the gas rarefaction for several values of the mole fraction and for two values of the wall speed. The smaller value of the speed corresponds to the limit when the nonlinear terms are negligible, while the larger value describes a nonlinear flow. The shear stress, velocity gradient, temperature, and mole fraction profiles are presented. The reported results can be used as benchmark data to test model kinetic equations for gaseous mixtures. To study the influence of the intermolecular potential, the same simulations are carried out for the hard sphere molecular model. A relative deviation of the results based on this model from those based on the ab initio potential are analyzed. It is pointed out that the difference between the shear stresses of the two potentials for the linearized solution is within 1%, while it reaches 6% for the nonlinear cases.