We present the theory of the fling step and a theoretical method for simulating accurately the near‐fault strong motions, and apply it to reproduce various strong‐motion records near surface faults. Theoretically, the fling step is the contribution of the static Green’s function in the representation theorem (Hisada and Bielak, 2003), and we show that this theory holds for any seismic velocity structure. We first demonstrate the validity of this theory using theoretical solutions of a circular fault model in a homogeneous full‐space. Next, we apply the theory to layered half‐spaces, present a theoretical method based on the wavenumber integration method, and introduce various techniques to simulate the near‐fault ground motions including fling steps with high accuracy. Finally, we demonstrate the effectiveness of the method by reproducing various strong‐motion records near surface fault ruptures and discuss the characteristics of near‐fault strong motions including the fling step and the forward directivity pulse. We made all of the software and data used in this article available on the internet.

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