The SAW reflection from a strip (Pt, Al) deposited on a half-infinite substrate (Z-cut AlN) is numerically studied. The strip-substrate contact forms an acoustic waveguide supporting leaky modes propagating faster than SAW on the free surface of the substrate. The excitation of a leaky mode by SAW leads to a singular behavior of the reflection and the transmission coefficients. The dependence is investigated of the magnitude and the phase of these coefficients on the angle of incidence, the frequency, the width and the thickness of the strip. Two types of leaky waveguide modes are considered: Love-wave type mode and LLSAW type mode.