In laser cutting of glass with controlled fracture, thermal stress induces a fracture and the material is cleaved along the cutting path by fracture propagation. Compared with CO2 laser, YAG laser has many advantages in cutting glass with controlled fracture. As a volumetric heat source, YAG laser can penetrate through the glass. Therefore, the temperature distribution is uniform across the thickness of the glass and the fracture propagates from the top and bottom surface to the middle so that better cutting quality can be acquired and multi-layer glasses can be cut simultaneously. In this paper, a 1064nm YAG laser is applied to cut two-layer and four-layer glasses. Fracture propagation mechanism is studied by examining the temperature and stress fields using finite element software ANSYS11.0. Good cutting qualities of fracture surfaces for all the layer glasses are acquired and the cutting efficiency is greatly improved by this technique as well. Additionally, due to smaller laser spot size the glasses that are closer to the focal point have higher laser power density inside glass, which may lead to ablation and evaporation phenomenon. But lower laser power density is not enough for fracture initiation and expansion. Therefore, it’s important to find a proper laser power for all the layer glasses. Small tensile stresses on the top and bottom surfaces will make the material separate from up and down to middle, whereas the compressive stresses in the middle ensure stable fracture propagation. Moreover, the stable fracture propagation always lags behind the laser beam spot. High tensile stresses are distributed throughout the thickness of the glass in the leading and trailing edges, which leads to unstable fracture extension in the leading and trailing edges.