Excessive drilling forces can result in drill breakage, bone breakthrough, and thermal necrosis during bone drilling process. However, the effect of drilling process parameters, drill geometry parameters, and bone material type on drilling forces have not been fully investigated. Three designs of experiments are introduced separately to study single factor’s effect on drilling forces, identify significant geometry parameters and possible interactions for drilling forces, and formulate direct relationship between drilling forces and process parameters. The results show that thrust force and torque are increased with feed rate, drill diameter or web thickness. The effect of spindle speed, point angle, helix angle, and chisel edge angle on drilling forces is complex. The results also show that the drilling forces are affected by bone type significantly, which are highest for bovine cortical bone, and lowest for Sawbones 3401. The levels of significance of geometry parameters are identified and different for thrust force and torque, which can assist new surgical drill development. Quadratic regression equations obtained by response surface methodology can predict thrust force and torque accurately in a wide range of process parameters, which can be used to control drilling conditions for robot assisted surgeries to realize safe drilling.