A small blind internal thread (SBIT) is used to firmly fasten some functional components to the cover of 3C electronic products. The small internal thread is made in a blind hole using a fluteless forming tap (FFT) that does not produce chips. However, the four geometric parameters (tool width (W), tooth root diameter (D2), front-end diameter (Df) and tooth angle (θ)) for the FFT affect the thread filling rate (f) and the minimum torque (T) for the tapping process. This study reports a Box-Behnken design (BBD) using DEFORM-3D (finite element model) and MINITAB (regression analysis) software to tap 7075-T6 aluminum alloy using a small FFT to achieve a repeatable thread filling rate and minimum torque. The experimental results show that the BBD accurately predicts and simulate the thread filling rate for tapping 7075-T6 aluminum alloy. The modelling software and the experimental design for this study can be used to optimize the design of tools that are used in industrial production.