The interaction between surface wave and a surface breaking crack is studied using a novel fast modeling tool called peri-ultrasound that can model both linear and nonlinear ultrasonic response. This modeling approach is based on peridynamic theory. In this study, the surface wave is modeled by applying a triangular pulse excitation function on the surface of a large structure. The particle movements are simulated on both sides of the surface crack to investigate transmitted and reflected fields. This investigation shows that: (1) the computed amplitude spectra of the Rayleigh wave agrees with the experimental observation; and (2) the structure containing a surface breaking crack shows noticeable increase in its nonlinear behavior. The computed results have been also verified against the analytical solution for a half-plane problem made of homogenous, isotropic, linear elastic material (Lamb's Problem).