The tensile thermal stress generated by laser irradiation with forced cooling is critical in the cleavage processing of thin plate glass. In this study, we predicted the conditions for generating tensile thermal stress in laser-induced cleavage of thin plate glass using numerical models from the viewpoint of the cooling and heating areas. An unsteady two-dimensional model was used to predict the temperature distribution and an unsteady plane stress model was used to predict the thermal stress. To generate tensile thermal stress, a cooling area is required behind the heating area. A specific scanning speed is required to yield the maximum tensile stress between the heating and cooling areas. A weak heat transfer coefficient in the cooling area generates tensile thermal stress only in the direction perpendicular to (y direction) the scanning direction of the heat source (x direction). A strong heat transfer coefficient generates tensile thermal stress in both the x and y directions. These tensile thermal stresses are surrounded by horseshoe-shaped compressive thermal stress. The tensile thermal stress can be controlled by selecting an appropriate cooling method for the cooling area.