A finite-element method was used to simulate the wave propagation of laser-generated ultrasound and its interaction with surface-breaking cracks in an elastic material. The thermoelastic laser line source on the material surface was approximated as a shear dipole and loaded as nodal forces in the plane-strain finite element (FE) model. The shear dipole FE model was tested for the generation of ultrasound on the surface with no defect. The model was found to generate the Rayleigh surface wave and to give the correct directivity patterns for longitudinal and shear bulk waves. The model was then extended to examine the interaction of laser-generated ultrasound with surface-breaking cracks of various depths. Both fixed and scanning laser sources (SLS) were considered. For the case of the fixed source, the crack-reflected Rayleigh waves were monitored to detect a crack. In the SLS technique, the laser-generated signal arriving at the Rayleigh wave speed was monitored as the laser source was scanned. The proposed model clearly reproduced the experimentally observed features that can be used to characterize the presence of surface-breaking cracks.