The 2001 Big Bear Lake earthquake (Mw 4.63) was recorded by over 30 strong-motion instruments in the San Bernardino basin region of southern California. At periods longer than about 1 sec, the ground motions in the central portion of the basin have significantly larger amplitudes and extended durations of strong shaking relative to sites outside the basin. In many cases, the peak motions at the basin sites occur 10 or more seconds after the direct S-wave arrival, suggesting that these arrivals are controlled by basin-generated surface waves. To model these motions, I have performed finite-difference simulations using a 3D representation of the basin velocity structure. The basin structure has a minimum shear velocity of 250 m/sec, which coupled with the model grid spacing of 50 m yields a bandwidth resolution limit of T>1 sec for the numerical simulations. The simulations do quite well at reproducing the observed waveforms, amplitudes, and durations at periods of 3 sec and longer. At shorter periods (1–2 sec), the fit to the recorded motions is less well resolved, especially in matching the waveforms of the later-arriving phases. This suggests that in regions of complex geology, deterministic waveform modeling at periods approaching 1 sec involves more than simply reducing the minimum velocity threshold and, in particular, requires knowledge of the subsurface structure and distribution of seismic velocities at relatively short length scales (on the order of 50 m).