We present measurements of the transmission of terahertz radiation through periodic arrays of holes made in highly doped silicon wafers. The size of the holes, 70\ifmmode×\else\texttimes\fi70\ensuremathμm,70\ifmmode\times\else\texttimes\fi{}70\ensuremath{\mu}\mathrm{m}, is significantly smaller than the radiation wavelength \ensuremathλ\ensuremath≃500\ensuremathμm.\ensuremath{\lambda}\ensuremath{\simeq}500\ensuremath{\mu}\mathrm{m}. Sharp resonances and enhanced transmissions are observed. This unusual transmission is attributed to the resonant tunneling of surface-plasmon po