A velocity slip on a mixed slip surface oscillating parallel to itself in a Newtonian incompressible liquid is numerically and theoretically studied. An unsteady Stokes equation is solved for the fluid flow induced by the sinusoidal oscillation of no-slip infinite flat plate involving a free-slip circular region in a finite-difference manner. The asymptotic solutions for a mixed boundary value problem are found through Hankel’s transforms or through self-similar scalings in the limits of the low and high driving frequencies. The velocity slip on the free-slip area is evaluated, and its frequency response is discussed.