Experimental results are presented for the downslope propagation of acoustic normal modes in a shallow water wedge with a penetrable bottom and a slope of up to 9°. A 7‐element line source was used to generate individual low‐order normal modes. To obtain single modes in a wedge it was necessary to align the line source to form an arc of a circle centered on the wedge apex. The resulting normal modes propagate with wave fronts which are also curved into arcs of circles centered on the wedge apex. These ‘‘wedge modes’’ propagate without coupling. The amplitudes, mode functions, and group velocities of the wedge modes are described by simple adiabatic normal mode theory, but the wave front curvature is not.