The recent by fly-bys of Oumuamua and Borisov suggest a large space density of such interstellar asteroids and comets. I investigate the possibility of capturing such objects into the Solar system via a fly-by of Jupiter or Saturn, presenting analytical arguments and estimates as well as results of various numerical simulations. The most likely captures occur for an incoming speed of around 0.6 km/s and populate orbits akin to those occupied by long-period comets. We estimate that the Solar system may contain around 10000 captured Oumuamua-like asteroids and 100 captured comets.