The electrochemical discharge machining (ECDM) process has a potential in the machining of silicon nitride ceramics. This paper describes the development of a second order, non-linear mathematical model for establishing the relationship among machining parameters, such as applied voltage, electrolyte concentration and inter-electrode gap, with the dominant machining process criteria, namely material removal rate (MRR), radial overcut (ROC) and thickness of heat affected zone (HAZ), during an ECDM operation on silicon nitride. The model is developed based on response surface methodology (RSM) using the relevant experimental data, which are obtained during an ECDM micro-drilling operation on silicon nitride ceramics. We also offer an analysis of variance (ANOVA) and a confirmation test to verify the fit and adequacy of the developed mathematical models. From the parametric analyses based on mathematical modelling, it can be recommended that applied voltage has more significant effects on MRR, ROC and HAZ thickness during ECDM micro-drilling operation as compared to other machining parameters such as electrolyte concentration and inter-electrode gap.Keywords ANOVA 9 Micro-electrochemical discharge machining (ECDM) 9 Response surface methodology (RSM) 9 Silicon nitride