Current research studies devoted to cutting forces in drilling are oriented toward predictive model development, however, in the case of mechanistic models, the material effect on the drilling process itself is mostly not considered. This research study aims to experimentally analyze how the machined material affects the feed force (Ff) during drilling, alongside developing predictive mathematical–statistical models to understand the main effects and interactions of the considered technological and tool factors on Ff. By conducting experiments involving six factors (feed, cutting speed, drill diameter, point angle, lip relief angle, and helix angle) at five levels, the drilling process of stainless steel AISI1045 and case-hardened steel 16MnCr5 is executed to validate the numerical accuracy of the established prediction models (AdjR = 99.600% for C45 and AdjR = 97.912% for 16MnCr5). The statistical evaluation (ANOVA, RSM, and Lack of Fit) of the data proves that the drilled material affects the F_f value at the level of 17.600% (p < 0.000). The effect of feed represents 44.867% in C45 and 34.087% in 16MnCr5; the cutting speed is significant when machining C45 steel only (9.109%). When machining 16MnCr5 compared to C45 steel, the influence of the point angle (lip relief angle) is lower by 49.198% (by 22.509%). The effect of the helix angle is 163.060% higher when machining 16MnCr5.