The rate and direction of rift propagation through ice shelves depends on both the stress field and the heterogeneity, or otherwise, of the physical properties of the ice. The Brunt Ice Shelf in Antarctica has recently developed new rifts which are being actively monitored as they lengthen and interact with the internal structure of the ice shelf. Here we present the results of a ground-penetrating radar survey of the Brunt Ice Shelf aimed at understanding variations in the internal structure. We find that there are flow bands composed mostly of thick meteoric ice interspersed with thinner sections of ice shelf that have a large proportion of sea ice and sea-water-saturated firn. Therefore the ice shelf is, in essence, a series of ice tongues cemented together with ice mélange. The changes in structure are related both to the thickness and flow speed of ice at the grounding line and to subsequent processes of firn accumulation and brine infiltration as the ice shelf flows towards the calving front. It is shown that rifts propagating through the Brunt Ice Shelf preferentially skirt the edges of blocks of meteoric ice and slow their rate of propagation when forced by the stress field to break through them.