The only alkali metal known to be superconducting at ambient pressure is Li at 0.4 mK. Under 30 GPa pressure textit{T}$_{c}$ for Li rises to 14 K. In addition, nearly 50 years ago the heavy alkali metal Cs was reported to become superconducting near 1.3 K at 12 GPa. In the present experiment the superconductivity of Cs under pressure is confirmed. In addition, strong evidence is presented in electrical resistivity measurements that neighboring Rb also becomes superconducting near 2 K at 55 GPa as it enters the textit{oC}16 phase, as for Cs, where textit{T}$_{c}$ decreases under the application of pressure. It would seem likely that under the right temperature/pressure conditions all alkali metals, including metallic hydrogen, will join the ranks of the superconducting elements. With the addition of Rb, 55 of the 92 naturally occurring elements are superconducting at ambient or high pressure.