Near-fault earthquake ground motion can be strongly enhanced relative to more distant sites, due to both the proximity of the source and the presence of pronounced directivity effects. Reliable predictions of these motions are impeded by the scarcity of near-source recordings for large earthquakes. Numerical simulations can play a useful role in quantifying near-source effects for use in engineering studies. In order to provide credible near-source ground motion estimates, simulations will need to account for the effect of reduced strength on the dynamics of rupture and slip on the shallow part of faults. While the numerical methods underlying dynamic earthquake simulations have frequently been tested against analytic solutions to linear problems, few opportunities exist to validate the methods for appropriate nonlinear, frictional-interface problems. Researchers have constructed foam rubber scale models of earthquakes which include a weak zone in the shallow part of the fault, and these controlled experiments provide detailed, subsurface recordings of rupture propagation and fault motion unavailable for real earthquakes. I show here that 3D finite difference (FD) simulations can replicate the main dynamic features observed in the physical models. There is notable similarity between physical and numerical models in rupture velocity and slip acceleration time histories on the fault. Local rupture velocities typically agree within 10%, with maximum discrepancies of 25%. Peak accelerations typically match within 40%, with maximum discrepancies of approximately a factor of two. In both models, peak acceleration is greatly diminished near the fault when the weak zone is present (relative to motion in the absence of the weakened zone), and the reduction factor scales up with weak zone thickness. Numerical simulations aid in the physical interpretation of the foam rubber experiments and can extend their parameter range. The results show that the lateral distance over which ground motion parameters are diminished increases with the depth of the weak zone. They further show that ground acceleration is sensitive to the strength of the weak zone, with decreased weak-zone strength leading to stronger ground motion. The ability of the numerical simulations to mimic key behaviors of the physical model provides a good starting point for simulation-based interpretation of earthquake ground motion recordings. Additionally, through parallelization of the computer code and the use of multiprocessor supercomputers, models can now be larger than previously possible. Larger FD models can accommodate a greater dynamic range of wavelengths, leading to better approximations of the underlying physics, and increasing the range of practical applications.