A thermal-stress field of laser drilling ceramic is calculated by building a two-dimensional (2D) thermal field model. Two types of cracks during pulsed laser drilling are predicted. One is along radial direction, and the other is along tangent direction. Further more, spreading characteristics of two types of cracks, emanative and regressive, during pulsed laser cutting are analyzed and predicted. It is concluded that the restraint of cracks can be achieved by reducing temperature of processing point, decreasing size of heat affected zone and increasing hole diameter (or kerf width). Based on analyzing parameters of the theoretical model, relationships between model parameters and processing parameters are discussed. It is proposed that optimizing laser processing parameters should depend on lower duty cycle, higher gas pressure and focal position outside the workpiece. The prediction results of crack formation and spread analyzed by the mathematic model are accordant with the experimental results of laser drilling and cutting of alumina ceramic and single-crystal silicon. Laser crack-free processing of ceramics is achieved by optimizing laser processing parameters based on the theoretical model.