Sodium substituted samples of $Y_{1-x}Na_xBa_2Cu_3O_{7-y}$ for $0.00{leq}x{leq}0.16$ were prepared and characterized by X-ray powder pattern, electrical resistivity and magnetic susceptibility measurements, Raman spectroscopy, and idometric titration. The Na substituted compounds have narrow solid solution limits where $0.00{leq}x{leq}0.16.$ As the Na concentration increases, the parent orthorhombic structure tends to gradually change to tetragonal. Small changes in the superconducting transition temperature, Tc, are observed in this solid solution region. Raman spectra for the Na phases are virtually identical with that of $YBa_2Cu_3O_7$ except that the Cu(1)-O(4) stretching mode at 504 $cm^{-1}$ and the Cu(2)-O(2,3) bending mode at 340 $cm^{-1}$ for x = 0.16 are slightly shifted. The hole concentrations of the sodium substituted compounds ranged from 0.31 to 0.33 per Cu site are increased with Na content. The substitution of $Na^+$ for $Y^{3+}$ site appears to create oxygen vacancies in the Cu-O chains, causes structural change from orthorhombic to tetragonal, and increases hole concentration in the substituted system.