The small blind internal thread (SBIT) plays a very important role to firmly fastening some functional components on the cover of 3C electronic products. The small internal thread was made in a blind hole using a fluteless forming tap (FFT) without producing chips. However, the four geometric parameters of the FFT (tool width (W), tooth root diameter (D2), front-end diameter (Df), and tooth angle (θ)) will affect the thread filling rate (f) and minimum torque (T) in tapping process. This study reports the Box-Behnken design (BBD), combined with DEFORM-3D (finite element model) and MINITAB (regression analysis) software, to tap 7075-T6 aluminum alloy with small FFT to obtain reliable results of thread filling rate and minimum torque. The experimental results show that the BBD can accurately predict and simulate the thread filling rate of tapping 7075-T6 aluminum alloy. The modeling software and experimental design used in this research are very suitable for the optimal design of the FFT used in industrial production.