This paper focus's upon the derivation of the similarity solutions of a free boundary problem arising in glaciology. With reference to shallow ice sheet flow we present a potential symmetry analysis of the second order non-linear degenerate parabolic equation that describe non-Newtonian ice sheet dynamics in the isothermal case. A full classical and also a non-classical symmetry analysis is presented. A particular example of a similarity solution to a problem formulated with Cauchy boundary conditions is described. This demonstrates the existence of a free moving boundary and also an accumulation-ablation function with realistic physical properties
