In this paper we address the issue of a creeping wave by investigating a twodimensional configuration which involves a surface-braking crack in a traction free planar backwall. We assume that this back-wall is irradiated by a shear Gaussian beam which is incident at a critical angle and hits the wall away from the crack edge. We show that the generated wave - known in the engineering literature as ”creeping”, because it propagates near the surface - consists of non-geometrical waves, the longitudinal and transverse components of the head wave and a longitudinal Goodier-Bishop type wave whose amplitude grows linearly with the distance to its propagation path. The ”creeping” wave interacts with the crack edge but the resulting field cannot be simulated using the Kirchhoff Approximation, because this does not embrace the higher order effects. We show that the diffracted field can be simulated using a modification of the Uniform Geometrical Theory of Diffraction which involves a relatively simple limiting procedure