The propagation characteristics of exchange‐free magnetoelastic (ME) Rayleigh waves are treated for the case of propagation on a YIG substrate that is magnetized perpendicular to its surface. As a result of the wave anisotropy of the constituent ME plane waves, these waves differ substantially from the ME Rayleigh waves propagating on a YIG substrate along or obliquely to a tangential bias field. Computed dispersion and polarization properties are presented for a low saturation magnetization Ga‐YIG substrate whose surface is eitherunmetallizedormetallizedwith a thin perfectly conducting metallic film. In either case, the dispersion diagram consists of two branches, one of which represents bound surface waves for frequencies below a spectrum of frequencies given approximately by the magnetostatic bulk‐wave spectrum, and the other branch represents bound surface waves for frequencies above this spectrum. Within the spectrum the surface waves are of the leaky variety, and can be used to obtain beam steering over an angle of 90 ° in the forward direction.