We estimated the possible range of long-period ground motion for sites located on a soft sedimentary basin in the immediate vicinity of a large earthquake. Since many large cities in the world (e.g., Los Angeles, San Francisco, and Tokyo) where many large structures have been recently constructed are located in this type of environment, a better understanding of long-period ground motion is becoming increasingly important. Our objective is to estimate the possible range of long-period ground motion, rather than ground motion for a specific fault model. We computed ground-motion time series and pseudo-velocity response spectra (PVS) for more than 5,000 models for the 1923 Kanto, Japan, earthquake (MW = 7.9) using 180 slip distributions, eight rupture geometry, and rupture velocities ranging from 1.5 to 3.0 km/sec. Two seismograms recorded in Tokyo during the 1923 Kanto earthquake are used for comparison. The response spectra computed using seismologically reasonable sets of source parameters for the 1923 Kanto earthquake vary by more than an order of magnitude. At periods of 10 to 13 sec, they range from 25 to 170 cm/sec in Tokyo. For some combinations of model parameters, the response spectra exhibit peaks in the range of 10 to 13 sec. Many of the computed response spectra have peaks at periods longer than 10 sec, which is considerably longer than the dominant period (6 to 8 sec) estimated from studies of small earthquakes and microtremor measurements. Thus, the dominant period of the subsurface structure determined locally may not be representative of the dominant period of ground motion from a nearby large earthquake, which is controlled by rupture directivity and source depth. We performed a similar simulation for a hypothetical MW = 7.5 earthquake located beneath the Los Angeles basin. For a site just above the center of the fault, the ground-motion spectral amplitude at a period of 10 sec can vary from 50 to 350 cm/sec. This range, though very large, is what is expected for a seismologically plausible range of source parameters.