This thesis is broken down into two parts, both of which are focused on the mechanics of subglacial hydrology. The first part describes the opening behavior of a crack under a supraglacial lake, where a Finite Element Method model is presented to obtain the opening profile of a crack undergoing hydrostatic tension in an infinite power law creep material. The second part focuses on creating a numerical model for the opening diameter of Röthlisberger channels in ice stream shear margins, where antiplane strain rates are superimposed on in-plane stresses.