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High-pressure torsion (HPT) is an established material strengthening technique through severe plastic deformation. Expanding its strengthening capabilities requires an appropriate deformation control. Unlike the thoroughly reviewed associated strengthening parameters like sample and processing variables, limited information concerning the apparatus variables is available due to the high experimental cost. This limitation was addressed in this present work by conducting parametric analysis through finite element simulation. This study examined the effects of anvil parameters, including the free flow gap between anvils, anvil wall inclination angle and anvils alignment, on the stress characteristics during HPT. The systematic analysis revealed that the free flow gap, j of 1 mm, leads to a heterogeneous pressure distribution across the sample radius. However, the pressure homogeneity depends slightly on the wall inclination angle, β . In particular, j ≤ 0.2 mm and β ≤ 10° could generate continuous strengthening behaviour with the applied strain. Furthermore, misalignment also demonstrated contributing to the disc centre strengthening, a critical explanation that the fundamental torsion test formula could not describe. The presented parametric analysis through a computer-aided numerical computation serves as an effective deformation control and optimisation. It complements the existing theory and experimental findings at a minimal computation cost. [ABSTRACT FROM AUTHOR]