In the CDM scenario, dark matter halos are assembled hierarchically from smaller subunits. A long-standing problem with this picture is that the number of sub-halos predicted by CDM simulations is orders of magnitudes higher than the known number of satellite galaxies in the vicinity of the Milky Way. A plausible way out of this problem could be that the majority of these sub-halos somehow have so far evaded detection. If such 'dark galaxies' do indeed exist, gravitational lensing may offer one of the most promising ways to detect them. Dark matter sub-halos in the 10⁶ - 10¹⁰M mass range should cause strong gravitational lensing on (sub-)milliarcsecond scales. We study the feasibility of a strong lensing detection of dark sub-halos by deriving the image separations expected for density profiles favoured by recent simulations and comparing these to the angular resolution of both existing and upcoming observational facilities. We find that there is a reasonable probability to detect sub-halo lensing effects in high resolution observations at radio wavelengths, such as produced by the upcoming VSOP-2 satellite, and thereby test the existence of dark galaxies.