Owing to its various distinct advantages over the other machining technologies, abrasive jet machining has become a promising machining technology for brittle and hard-to-machine materials. An experimental study is presented on the micro-grooving of quartz crystals using an abrasive airjet. The effect of the various process parameters on the major machining performance measures are analysed to provide a deep understanding of this micro-machining process. Predictive models are then developed for quantitatively estimating the machining performance. The models are finally verified by an experiment. It shows that the model predictions are in good agreement with the experimental results under the corresponding conditions.