The new non-conventional cutting process by the use of thermal shock is a convenient procedure for cutting the brittle materials such as glasses and ceramics. This method is based on the application of localized thermal shock to brittle materials by the use of hot air jet, which induces thermal stresses at the tip of an existed pre-crack. Due to the thermo-elastic behavior of materials, the pre-crack is propagated in the material. By the use of this process, the glass and brittle materials can be cut to any shape without the use of cutting tools. In this paper, based on the presented phenomena and the induced time-dependent thermal shock, the tip of an existed pre-crack in a glass sheet is heated by a moveable point heat source. The effect of parameters such as cutting speed, nozzle orifice diameter, cutting temperature, macroscopic quality of cutting surface on cutting the brittle materials were studied. The results indicated that as far as a pre-defined distance is developed between the moveable heating point and the tip of the existed pre-crack, the crack is propagated in stable manner and under complete control, and hence better cutting surface quality. Based on this distance, the effective cutting parameters are investigated and set to get better cutting process.