Magnesium alloys are one of the crucial engineering materials and are alternative to aluminum and steel due to their superior properties. In this paper, drilling of AZ31 magnesium alloy was investigated and cutting parameters with multiple performance charecteristics were optimised with grey relational analysis. Effects of machining parameters such as cutting speed, feed rate, cutting tool material and their interactions on the thrust force, surface roughness and hole quality were determined. The Taguchi L-27, 3-level, 3-factor orthogonal array was used for the tests. The analysis indicated that feed rate and drill material had higher effective parameters than spindle speed. Furthermore, the results revealed that optimal combination of the drilling parameters can be used to obtain the minimum thrust force, surface roughness and size error.