Drilling of ceramic material reinforced Metal Matrix Nanocomposites (MMNCs) become very challenging as the hard and brittle ceramic material embedded inside the matrix. Also, the burr formation after drilling is quite obnoxious as extra manufacturing cost is associated with the removal of those burrs. Moreover, literature on optimization of drilling characteristics of Al-Si3N4 metal matrix nanocomposites (MMNCs) is not available. Present study tries to remit that literature gap. In present study, ultrasonic vibration assisted stir casting (USC) method is used to fabricate Al-Si3N4 MMNCs. Basic characterizations are done with the aid of Optical Microscope (OM), Scanning Electron Microscope (SEM) and Energy Dispersive X-ray Analysis (EDX). SEM micrographs vindicated homogeneous distribution of Si3N4 particles inside composite matrix. EDX result justifies the manifestation of Si3N4 particles into the composites. Afterwards effects of process parameters, i.e., wt.% of reinforcements, drill point angle, feed rate and speed, on burr height and width are examined using Taguchi method and Grey relational analysis. Analysis of variance (ANOVA) is also performed to find significant and evocative process parameters. Increasing order of reinforcement shows minimization of drill burr height and width with and improvement of S/N ratio of 122.53% and 54.60% respectively. Wt.% and feed are found to be most significant parameters corresponding to burr height and burr width respectively. Finally, confirmation study is performed to corroborate the developed model. Confirmation table reveals that burr height and burr width are improved by 122% and 60% respectively.