A full 3-D transient model is developed for the ablation phenomena and thermal stress evolution during laser cutting and/or drilling of ceramic plates. The computational methodology is based on the Galerkin finite element method along with the use of a fixed grid algorithm to treat the thermal ablation resulting from an applied laser source. The present model is able to model any complex ablation operations involving discontinuity in geometries, as encountered in laser cutting and laser drilling operations. This is an advantage over the front tracking method by which the ablation moving interface is precisely tracked in time and which is useful for simple geometries. The laser ablation model is coupled with a thermal stress model to predict the evolution of thermal stresses, which arise due to a rapid change in thermal gradient near the laser beams. Model predictions compare well with the available data in literature for a simple configuration. Results obtained from model for both dual pulsed laser cutting and single laser drilling are discussed.