Abrasive jet machining is widely used for shaping hard, difficult-to-machine materials. Material is removed by a high velocity stream of a mixture of gas and abrasive particles which impact on the surface of a material to erode the material as required. Optimization of material removal rate (MRR) as well as nozzle wear rate are possible by deciding appropriate range of factors like rate of abrasive flow, its grain size, system pressure and stand-off distance. Experiments have been designed with Box–Behnken method of response surface methodology and the analysis is done using Minitab 2017. Drilling is carried out on a commercially pure 4 mm thick alumina specimen using silicon carbide abrasive. After performing analysis of variance (ANOVA), significance of individual parameter and their interactions are found out in terms of judging ‘p’ value with more than 95% confidence level. The working jet pressure contributes significantly on MRR through impact erosion. It has been noted that as system pressure increases, MRR and nozzle wear rate show an increasing tendency.