The linear and nonlinear response of a plasma sheath is studied by subjecting it to rf potentials at frequencies corresponding to certain natural modes of oscillation of the sheath‐plasma system. The sheath investigated is one that exists around a spherical dipole probe, immersed in an essentially collisionless uniform plasma and excited with sinusoidal signals at frequencies between 50 and 250 MHz. It is shown that the linear rf current‐voltage characteristics agree with both the simple sheath model of Mayer and Harp and with the more refined model of DeAngelis and Baldwin. The nonlinear response (which is observed as the generation of higher harmonics) is quantitatively explained as being due to an oscillation of the sheath‐plasma boundary induced by the applied rf field. This oscillation, in effect, acts as a time varying sheath capacitance.