We present the results of a wide‐angle seismic survey, consisting of a grid of five strike and three dip profiles, conducted in Bransfield Strait, Antarctica. We used a combination of two‐dimensional seismic tomography and ray tracing to constrain velocity structure in the region. Thinnest crust is located within the interpreted neovolcanic zone, but the crustal thickness of 10–15 km indicates that rifting has not progressed to the formation of normal oceanic crust. Crust thickens to 20–26 km along the South Shetland Islands pedestal and to 14–20 km along the Antarctic Peninsula margin. Along‐strike, crust generally thickens from the NE to the SW. In the across‐strike direction, crustal thinning is observed over a broader area in the NE than in the SW. The observed crustal thickness pattern is consistent with propagation of extension from the NE toward the SW. Upper mantle velocities of 7.45 ± 0.2 km/s indicate either the presence of a small amount of partial melt or normal upper mantle anisotropy with the slow direction parallel to the rift axis. Large lateral changes in upper crustal velocities along the Antarctic Peninsula margin correspond with seismically imaged structural boundaries. There is no correlation between these structural boundaries and large velocity changes or morphologic steps observed within the present‐day neovolcanic zone. We suggest that the rift topography now characterizing the Antarctic Peninsula margin formed prior to the formation of the modern basin.