An acoustic touch apparatus is provided that includes a substrate capable of propagating surface acoustic waves, such as Rayleigh-type or Love-type waves. The substrate has a front surface, a back surface, and a curved connecting surface formed between the front surface and the back surface. The apparatus also includes at least one acoustic wave transducer and at least one reflective array, the acoustic wave transducer and the reflective array behind the back surface of the substrate. The acoustic wave transducer is capable of transmitting or receiving surface acoustic waves to or from the reflective array. The reflective array is capable of acoustically coupling the surface acoustic waves to propagate from the back surface and across the front surface via the curved connecting surface. Various types of acoustic touch apparatus with edge sensitive touch functions can be provided, according to specific embodiments.