We introduce a plasmonic analog for the dynamics of a quantum particle under a linear restoring force bouncing off an impenetrable barrier (“quantum paddle ball”). Paddle-ball-type plasmonic potentials are constructed in quadratically modulated metal-dielectric-metal structures with transverse metallic reflecting walls. We show, both analytically and numerically, the full-wave nature of the phenomenon, including plasmon bouncing and complete wave revivals after interference at the boundary. We show that the plasmon paddle-ball dynamics is effectively wavelength independent, opening opportunities for subwavelength manipulations of polychromatic and ultrashort-pulse plasmons.