The micro electrical discharge machining (μ-EDM) process is extensively applied for micro-hole drilling in difficult-to-cut materials used in industries including aerospace, automotive, and biomedical. However, the slow material removal and challenges in drilling deep holes, limits the wide range applications of μ-EDM. Although, several research proposed approach of workpiece vibration to improve the process performance, the ambiguity remains towards the influence of vibration on process outputs. In this work, experiments were conducted to assess effectiveness of vibration in improving machining rate, and depth, overcut and surface quality of drilling holes. It was witnessed that in absence of tool wear compensation, vibrating the workpiece does not significantly improve maximum attainable depth, however, it helps in drilling the hole faster. Entry side hole overcut was highly stochastic in nature and not significantly affected by vibration. On the machined surface, spillover from molten pool due to vibration is observed for material with higher conductivity. For modelling the outputs of this complex hybrid process, a previously unused technique- Gaussian Process Regression (GPR) is tried and found that it predicts with greater accuracy than multivariate regression technique. © 2022 The Authors