  Strong gravitational lenses provide an important tool to measure masses in
the distant Universe, thus testing models for galaxy formation and dark matter;
to investigate structure at the Epoch of Reionization; and to measure the
Hubble constant and possibly w as a function of redshift. However, the limiting
factor in all of these studies has been the currently small samples of known
gravitational lenses (~10^2). The era of the SKA will transform our
understanding of the Universe with gravitational lensing, particularly at radio
wavelengths where the number of known gravitational lenses will increase to
~10^5. Here we discuss the technical requirements, expected outcomes and main
scientific goals of a survey for strong gravitational lensing with the SKA. We
find that an all-sky (3pi sr) survey carried out with the SKA1-MID array at an
angular resolution of 0.25-0.5 arcsec and to a depth of 3 microJy / beam is
required for studies of galaxy formation and cosmology with gravitational
lensing. In addition, the capability to carryout VLBI with the SKA1 is required
for tests of dark matter and studies of supermassive black holes at high
redshift to be made using gravitational lensing.
