We present simple deterministic process models for the prediction of the evolution of the cross-sectional profile of glass channels generated by erosive wear in micro air abrasive jet machining using a round nozzle. The present work was motivated by a need to understand the sensitivity of the geometry of the generated cross-sectional profile to the degree of offset between the centre of the nozzle and the centre of the mask defining the channel. Experiments were carried out on soda lime and borosilicate glass to verify the process models. Predicted results show fairly good agreement with experimental results. We conclude that, without proper alignment, the cross-sectional profile is easily skewed, as the micro abrasive jet machining process quickly acts on any initial geometrical skewness and compounds it over time.