[en] The excitation and propagation of lower-hybrid waves in an inhomogeneous, cylindrical plasma is studied theoretically for finite-length electrostatic sources. The boundary-value problem for the electrostatic potential in a cold, inhomogeneous plasma is solved numerically as a superposition of the radial eigenmodes excited by a finite-length source. Radial eigenmodes are found numerically by an algorithm which includes the case where the lower-hybrid resonance layer occurs in the plasma. The eigenmode superposition is carried out for several phased-ring sources. The plasma response is found to be composed of resonance-cone surfaces along which the potential is a maximum. When the resonance layer does not occur in the plasma, the resonance-cone surfaces reflect from the column axis and at the plasma boundary. For the case when the resonance layer does occur, the resonance-cone surfaces become asymptotic to the resonance layer and do not penetrate to the center. The presence of damping causes the resonance-cone singularities to dissolve axially leaving the lowest-order radial mode excited by the source