AA7075 aluminum alloy attracts scientific interest to participate in production of crucial components in aerospace, construction and automotive domains. Specifically, final products need to display equal quality to ensure the basic standards of safety in the aircraft industry. Despite the high machinability of the AA7075 alloy, hole quality may vary according to tool geometry and drilling parameters. In this study, the effects of different feed rate levels and cutting speeds on the surface roughness (Ra) and thrust (Fz) were investigated. Drilling experiments were conducted with drills of three different quality and geometry. The effects of drilling variables on the surface roughness and the thrust force according to "the smaller-the better" approach of the gray relation analysis (GRA) method have been investigated. Consequently, the highest and lowest gray relations degrees obtained were 0.828 and 0.338, respectively. Numerical analyzes for thrust force were performed with the ThirdWave AdvantEdge simulation software based on the finite element method. We also outlined that there exists an average difference of 4.9 % between the experimental and simulation thrust force values, and we proved the applicability of the finite element model.