Surface features of Enceladus, Tethys, Dione, Iapetus, Miranda, Ariel, and Titania indicate that these satellites, with radii from the range 252–879 km, are highly or at least moderately modified due to internal tectonic activity. Detailed studies of known surfaces show that Enceladus is probably still geologically active at present while Tethys, Dione, Miranda, Ariel, and Titania were active in the recent past. Convection is one of the processes responsible for the evolution of the bodies of Solar System, including the evolution of icy satellites. We focus on studying the possibility of convection within the medium sized icy satellites. Thermally driven convection of solid satellite material as potential cause of surface evolution is considered for two cases: non-differentiated icy-mineral satellites and differentiated satellites with icy mantle and rocky core. Discussion of the parameters of icy/rocky mixture indicates that the Rayleigh number is higher than critical value for onset of convection.