Laser material processing is an enabling technology that has resulted in revolutionary product designs as well as novel manufacturing practices that have improved quality, productivity and flexibility in industry. Laser technology has changed precision drilling capabilities in the manufacturing industries. The highly focused beam of collimated light emits energy allowing the laser to drill accurate patterns of holes into extremely difficult-to-machine materials such as ceramics. With drill contact eliminated, a minimal heat affected zone (HAZ), and narrow kerf, ceramics can be drilled without distortion of the finished product. Although the use of lasers for drilling of structural ceramics has increased rapidly in recent years, the failures due to high thermal stresses and brittleness of the ceramic structures are still a major problem for manufacturing industries. Figure 1 shows a cracked alumina plate after laser drilling. Temperature gradients that occur during laser-material interaction result in strong thermal stresses in the heat affected zone. Due to the high thermal stresses and short process time (nanoseconds), many micro- cracks initiate and propagate through the ceramic. Sometimes, if thermal stress is high enough, the ceramic can fail [1]. Previous theoretical studies have some models of the laser machining of ceramics [1,2]. Gross et. al. [2] investigated crack formation during laser drilling of silicon wafers.