Thermal evolution models of differentiated and undifferentiated ice-silicate bodies containing longlived radiogenic heat sources are examined. Lithospheric stresses arise due to volume change of the interior and temperature change in the lithosphere. For an undifferentiated case, the surface stress peaks early in the evolution, while in the differentiated case, stresses peak later and continue to accumulate for longer periods of time. The variation of near-surface stress with depth shows that stresses for the undifferentiated body intially penetrate to great depths, but rapidly concentrate within a few kilometers of the surface. For the differentiated body, elastic stresses never accumulate at a depth greater than a few kilometers. These models are applied to consider long-term radioactive heating as a possible mechanism of tectonic activity and bright terrain formation on Ganymede.