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• A 3D dynamic torsional impedance solution is derived for offshore large-diameter pipe piles. • The impedances across the pile cross-section vary with the pile dimension and soil plug strength. • One-dimensional rod theory overestimates the overall impedance of the cross-section. • For common-size pipe piles, the impedance decreases from the pile outer radius to the inner radius. • For large-diameter pipe piles, the soil plug could play a dominant role in resisting torsional vibrations. Wind-induced or current-induced torsional vibration is a long-neglected issue for offshore engineering (e.g., offshore wind turbines, offshore oil platforms, etc.). As the dimension of the pipe pile implemented offshore increases dramatically, the one-dimensional rod theory can no longer precisely compute the dynamic torsional impedance. This paper proposes a novel 3D torsional soil-pile interaction model and derives the corresponding analytical solution for the 3D dynamic torsional impedance at the pile cross-section with the adoption of the Laplace transform, variable separation, and impedance transfer method. The solution is then validated by comparisons against some widely-accepted existing solutions. The main conclusions of this study can be drawn as follows: (1). Classic one-dimensional theory overestimates the impedance of the pipe pile, which could result in severe disasters if the dynamic design is radical; (2). Even for small diameter pipe piles, the impedance would vary in the radial direction at the pile cross-section. Usually, the impedance at the outer radius would be slightly larger than that at the inner radius; (3). For large-diameter pipe piles or pipe piles with high-strength soil plugs, the most significant impedance could appear at the inner radius, indicating the resistance provided by the soil plugs can not be overlooked for large-diameter pipe piles. [ABSTRACT FROM AUTHOR]