The interface between two wedges can be treated as a displacement discontinuity characterized by elastic stiffnesses. By representing the boundary between the two quarter-spaces as a displacement discontinuity, coupled wedge waves were determined theoretically to be dispersive and to depend on the specific stiffness of the non-welded contact between the two wedges. Laboratory experiments on isotropic and anisotropic aluminum confirmed the theoretical prediction that the velocity of coupled wedge waves, for a non-welded interface, ranged continuously from the single wedge wave velocity at low stress to the Rayleigh velocity as the load applied normal to the interface was increased. Elastic waves propagating along the coupled wedges of two quarter-spaces in non-welded contact are found to exist theoretically even when the material properties of the two quarter-spaces are the same.