In this paper, the thrust force and surface roughness are predicted by response surface methodology (RSM) when drilling AZ31 magnesium alloys by using HSS and carbide tools. Taguchi's L18, 3-level, 3-factor orthogonal array was used for the tests. The influence of machining parameters and their interactions on the thrust force and surface roughness were argued in detail. The results revealed that feed rate and drill material had higher effective parameters than spindle speed. A second order model for the thrust force and surface roughness is determined considering the drilling parameters. Predicted and measured results are found to be sufficiently close to eachother indicating that the established model could be used for predicting the responses in drilling these magnesium alloys. The model is confirmed by using confirmation experiments.