A process of aborption of energy by a cold nonuniform collisionless plasma from an externally driven electric field is described using a linearized theory. With the example of a cylindrically symmetric plasma, power is shown to be absorbed whenever the maximum plasma frequency exceeds the driving frequency. The admittance of the plasma as seen by an external circuit is developed and found to be sensitively dependent upon the equilibrium density distribution near the wall, suggesting the use of this phenomenon to examine electron sheath structure. Experimental results are presented which support the theoretical prediction. The occurrence of this absorption in the presence of a magnetic field and its effect upon the propagation of surface modes along a nonmagnetized plasma column are also indicated.