The equation which describes the motion of an ice sheet under its own weight has a cylindrically symmetric similarity solution. The initial value problem of the equation of motion which has been linearized in the deviations from this similarity solution is solved by an expansion of the solution in terms of eigenfunctions of the linearized equation. The linearized equation determines, for all ice sheets of the same volume, an asymptotically stable motion. These results are compared with the corresponding results of the two-dimensional case (Halfar, 1981).