In this paper, a technique for measuring a surface wave transmission coefficient across surface-breaking cracks and notches in a heterogeneous but globally isotropic material (concrete) is presented. Once the transmission coefficient across a surface discontinuity is known, its depth may be estimated. There are many difficulties in measuring the transmission coefficient experimentally owing to effects of wave path dependence, unknown characteristics of the receiver and the wave source, and the variation of impact event or receiver coupling. To eliminate the undesired effects, a self-calibrating measurement scheme is applied to obtain the surface wave transmission coefficient across notches and surface-breaking cracks in concrete. The obtained signal transmission coefficient is not affected by the experimental setup or the heterogeneous nature of the material. The testing scheme is described and experimental results obtained from concrete specimens with notches and surface-breaking cracks are presented. Repeatable and reliable measurements of surface wave transmission coefficient are obtained, which demonstrate a strong relation to normalized discontinuity depth. A numerical study using the boundary element method is presented, which verifies the experimental findings.