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Supersonic flows around diamond airfoils, under large-amplitude step motion, are analytically studied. Nine regions with distinct flow structures are identified on each side. These regions include intricate wave structures and significantly shape the indicial response. The novelty of this work is to develop theoretical models, capable of describing each region’s wave speed, pressure, and force. We achieve this by correcting the linear solution to the problem and incorporating nonlinear effects of large angle and airfoil thickness. Our model reports good accuracy regarding the computational fluid dynamics. And three stages, which are predicted by this model, precisely capture important features of aerodynamic force evolution.