Based on the relationship between the features of laser ultrasonic waveform and the spatial distribution, temporal distribution of the laser pulse as well as the material physical properties, a model for the thermoelastic generation of ultrasonic wave in metals and non-metals is established by using finite element method (FEM). The temperature distributions in metal and non-metallic materials excited by laser pulse are obtained, and the ultrasonic waveforms at the epicenter caused by thermoelastic expansion are calculated by utilizing the temperature distributions as ultrasonic force source. The generation reason and rules of precursor are analyzed according to the waveforms at the epicenter. The results show that, because of the thermal diffusion, a force source is excited on the metal surface, whereas a body force source with relatively large depth is caused due to the optical penetration in non-metals. The stresses normal to surface are excited by rapid expansion of material heated by laser pulse, but the location that the stresses act on is below the surface in the case of non-metals, so the precursor is monopolor in metals and it becomes dipolar in non-metals. The precursor waveforms include the material physical properties and parameters, so this research is useful for nondestructive materials test and evaluation by utilizing the characteristic of precursor.