Foam rubber experiments simulating unilaterally propagating strike-slip earthquakes provide a means to explore the sensitivity of near-fault ground motions to rupture geometry. Subsurface accelerometers on the model fault plane show rupture propagation that approaches a limiting velocity close to the Rayleigh velocity. The slip-velocity waveform at depth is cracklike (slip duration of the order of narrower fault dimension W divided by S-wave speed β). Surface accelerometers record near-fault ground motion enhanced along strike by rupture-induced directivity. Most experimental features (initiation time, shape, duration and absolute amplitude of acceleration pulses) are successfully reproduced by a 3D spontaneous-rupture numerical model of the experiments. Numerical- and experimental-model acceleration pulses show similar decay with distance away from the fault, and fault-normal components in both models show similar, large amplitude growth with distance along fault strike. This forward directivity effect is also evident in response spectra: the fault-normal spectral response peak (at period ∼W/3β) increases approximately sixfold along strike, on average, in the experiments, with similar increase (about fivefold) in the corresponding numerical simulation. The experimental- and numerical-model response spectra agree with an empirical directivity model for natural earthquakes at long periods (near ∼W/β), and both overpredict shorter-period empirical directivity effects, with the amount of overprediction increasing systematically with diminishing period. We attribute this difference to rupture- and wavefront incoherence in natural earthquakes, due to fault-zone heterogeneities in stress, frictional resistance, and elastic properties present in the Earth but absent or minimal in the experimental and numerical models. Rupture-front incoherence is an important component of source models for ground-motion prediction, but finding an effective kinematic parameterization may be challenging.