In this letter, we present a technique to fluidically tune the responses of periodic structures with multiple unit cells and finite dimensions. The periodic structures are composed of subwavelength constituting unit cells. This technique is applied to a two-dimensional high-impedance surface with multiple unit cells, and the response of the structure is continuously tuned. The technique is based on embedding metal and glass balls inside several parallel channels within a dielectric substrate supporting the structure. In each channel, a periodic arrangement of metal and glass balls is assembled and is allowed to move freely within the channel. By moving this periodic train of balls over small distances with respect to the fixed periodic structure, the response of the structure is continuously tuned. Three-dimensional (3-D) printing technology is used to implement the dielectric substrate with embedded fluidic channels. An architecture for the fluid distribution network is proposed that ensures the movement of balls in all channels is synchronized. A prototype with 16 parallel channels accommodating several unit cells in each channel is fabricated, and synchronized movement of the balls is verified experimentally when the balls in channels are embedded in mineral oil and pressure driven. Using this substrate and an array of subwavelength capacitive patches fabricated on a thin dielectric substrate, a fluidically tunable high-impedance surface is designed and experimentally characterized.