A dense grid of ice-penetrating radar sections acquired over Pine Island Glacier, West Antarctica has revealed a network of sinuous subglacial channels, typically 500m to 3km wide, and up to 200m high, in the ice-shelf base. These subglacial channels develop while the ice is floating and result from melting at the base of the ice shelf. Above the apex of most channels, the radar shows isolated reflections from within the ice shelf. Comparison of the radar data with acoustic data obtained using an autonomous submersible, confirms that these echoes arise from open basal crevasses 50-100m wide aligned with the subglacial channels and penetrating up to 1/3 of the ice thickness. Analogous sets of surface crevasses appear on the ridges between the basal channels. We suggest that both sets of crevasses were formed during the melting of the subglacial channels as a response to vertical flexing of the ice shelf toward the hydrostatic condition. Finite element modeling of stresses produced after the formation of idealized basal channels indicates that the stresses generated have the correct pattern and, if the channels were formed sufficiently rapidly, would have sufficient magnitude to explain the formation of the observed basal and surface crevasse sets. We conclude that ice-shelf basal melting plays a role in determining patterns of surface and basal crevassing. Increased delivery of warm ocean water into the sub-ice shelf cavity may therefore cause not only thinning but also structural weakening of the ice shelf, perhaps, as a prelude to eventual collapse.