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.