The plane‐strain problem of the scattering of a Rayleigh wave by a thin surface strip is formulated in terms of a pair of coupled integral equations, one of which is singular. The equations are equivalent to a set of boundary conditions which represent the effect of the strip on the substrate. A technique based on Gaussian approximation of the integrals is employed to solve the equations numerically for two representative cases over a range of wavelengths. The power reflection and radiation coefficients and the phase of the reflected surface wave are evaluated for the representative cases.Subject Classification: [43]35.54; [43]20.15, [43]20.30.