The effects of the co-seismic static offset (known as fling step) and associated velocity pulses on civil structures have been difficult to study because the static offset is typically removed during the processing of earthquake ground motion records. Simulated ground motions contain fling features and require no processing; therefore, they create new opportunities for representing fling features in seismic hazard analysis and assessing their influence on the seismic demands on near-fault structures. We use physics-based fault rupture simulations to study the characteristics of ground motions with fling step and the sensitivity of the near-fault structural demands to strong fling features. We uncover that simulated ground motions with a large fling step tend to have higher spectral intensity than those without a fling step at the same rupture distance, especially at periods longer than 2 s. As a result, the structural demands on flexible buildings tend to be the most sensitive to the fling features. Statistical analysis suggests that the ground motion spectral shape (represented by spectral accelerations at multiple periods) is—in most cases—a sufficient predictor of the structural demands on near-fault low-rise and mid-rise buildings at locations that are susceptible to strong fling effects. Finally, ground motion record selection experiments reveal that representing the spectral shape features at periods that are most relevant to a given structure may be an effective strategy to reduce the bias in the estimated demands on near-fault long-period structures when the available database of records is considered deficient in fling features.