Fling is the engineering term for the effects of the permanent tectonic offset, caused by a rupturing fault in the recorded ground motions near the fault. It is expressed by a one‐sided pulse in ground velocity and a nonzero final displacement at the end of shaking. Standard processing of earthquake time histories removes some of the fling effects that may be required for engineering applications. A method to parameterize the fling‐step time history and to superimpose it onto traditionally processed time histories has been developed by Abrahamson (2002). In this paper, we first present an update to the Abrahamson (2002) fling‐step models, in which the fling step is parameterized as a single cycle of a sine wave. Parametric models are presented for the sine‐wave amplitude (D_site) and period (T_f). The expressions for D_site and T_f are derived from an extensive set of finite‐fault simulations conducted on the Southern California Earthquake Center broadband platform (see Data and Resources). The simulations were run with the Graves and Pitarka (2010) hybrid simulation method and included strike‐slip and reverse scenarios for magnitudes of 6.0–8.2 and dips of 30 through 90. Next, an improved approach for developing design ground motions with fling effects is presented, which deals with the problem of double‐counting intermediate period components that were not removed by the standard ground‐motion processing. Finally, the results are validated against a set of 84 empirical recordings containing fling.