The Antarctic Ice Sheet loses mass to the surrounding ocean mainly by drainage through a network of ice streams: fast-flowing glaciers bounded on either side by ice flowing one or two orders of magnitude more slowly. Ice streams flow despite low driving stress because of low basal resistance but are known to cease flowing if the basal conditions change, which can take place when subglacial sediment becomes dewatered by freezing or by a change in hydraulic pathways. Carlson Inlet, Antarctica has been interpreted as a stagnated ice stream, based on surface and basal morphology and shallow radar reflection profiling. To resolve the question of whether the flow history of Carlson Inlet has changed in the past, I conducted a ground-based radar survey of Carlson Inlet, the adjacent part of Rutford Ice Stream, and Talutis Inlet, West Antarctica. This survey provides details of the internal ice stratigraphy and allows the flow history to be interpreted. Tight folding of isochrones in Rutford Ice Stream and Talutis Inlet is interpreted to be the result of lateral compression during convergent flow from a wide catchment into a narrow, fast-flowing trunk. In contrast, the central part of Carlson Inlet has gently-folded isochrones that drape over the bed topography, suggestive of local accumulation and slow flow. A 1-D thermo-mechanical model was used to estimate the age of the ice. I conclude that the ice in the centre of Carlson Inlet has been near-stagnant for between 3500 and 6800 yr and that fast flow has not occurred there during that time period.