In this study, machinability of AZ 91D magnesium alloy, which has been widely used in automotive and aircraft industries, was investigated by using HSS and carbide tools at dry cutting conditions. Taguchi's L-18 (2**1 3**2) mixed model was used for the experiments. Drilling parameters such as feed rate, spindle speed and cutting tool were optimized according to the multiple responses (diametral error, circularity and surface roughness) by grey relational analysis. The effects of machining parameters and their interactions on the hole diameter, circularity and surface roughness were determined The analysis of Taguchi and ANOVA indicated that the influence of drill material on the surface roughness of the drilled hole was high, but on the hole diameter and circularity it was low. Furthermore, the results of grey relational analysis revealed that optimal combination of the drilling parameters (0.3 mm/rev feed rate, carbide tool and 3000 rpm spindle speed) can be used to obtain the minimum diametral error, circularity error and surface roughness.