An explicit calculation of the quantum nonlocal polarizability of a metallic nanowire is presented. The modification of the standard approach due to quantum nonlocal effects is included by employing the quantum hydrodynamic description of the electron density a well as the appropriate additional quantum boundary conditions. In the presence of the quantum tunneling effects, the main polarizability peak, due to the surface plasmon, blueshifted from its classical position and subsidiary peaks, due to the excitation of bulk plasmons, appear above the bulk plasma frequency.
