Determining the flow history of ice sheets is an issue central to glaciology. Stratigraphic ice horizons provide the only known natural markers for inferring velocity at depth. Stratigraphy can be detected by radio-echo sounding (RES, also called radar) and dated by coring, which together determine the age field in the ice. In this thesis it is shown for the first time how ice flow can be deduced from stratigraphy. As a first step a method is given for the deduction of the spatial pattern of accumulation from shallow dated stratigraphy. The effects of densification and horizontal divergence are determined. It is then shown how, and when, internal motion can be deduced from dated stratigraphy. A theory is developed to deduce streamlines assuming steady-state flow and mass conservation. The theory does not require rheological assumptions or a spatial accumulation rate pattern. The theory can be used to determine internal deformation rates, accumulation rate history and whether or not obs