Ceramics are being increasingly used in industry due to their outstanding physical and chemical properties. But these materials are difficult to machine by traditional machining processes, because they are hard and brittle. Recently, as one of various alternative processes, laser-beam machining is widely used in the cutting of ceramics. Although the use of lasers presents a number of advantages over other methods, one of the problems associated with this process is the uncertain formation of cracks that result from the thermal stresses. This paper presents a Bayesian probabilistic modeling of crack formation over thin alumina plates during laser cutting.