Solid state convection in the mantle of icy satellites of giant planets is investigated using numerical models. We consider differentiated and non-differentiated satellites with both free (that is no horizontal stresses) and rigid (that is zero velocity) boundary conditions at the body surface. Internal heating originates from long lived radioactive elements uniformly distributed within rocky component of satellites (with initial chondritic concentration). Two modes of internal heating by radioactive sources are considered: uniform distribution of radioactive elements within undifferentiated bodies and heating of the icy mantle by heat flux from the rocky core. The calculations were performed for the range of Rayleigh number from 10 000 to 300 000. It corresponds to the medium size icy satellites in radii from the range 200 – 800 km. We found that convection velocity of the order of 1 mm yr−1 is typical for considered bodies. This is at least one order of magnitude less than the velocity in the Earth's mantle but even such slow convection could be an important factor changing global tectonic activity, asymmetry of hemispheres, gravitational field and shape of the satellites.