The peak ground acceleration (PGA) and peak ground velocity (PGV) from 5058 ruptures of a foam rubber stick‐slip model are not distributed according to a lognormal probability distribution function. PGA and PGV values are decomposed using the method of Anderson and Uchiyama (2011). The statistically significant deviations from the lognormal distribution occur near the peak of the distribution. In some cases, high‐amplitude tails differ by a much greater ratio, but the statistical significance of this effect is low. This result is true of both raw data and data adjusted for site and magnitude. Event terms are also not lognormal but can be modeled as a sum of three or four lognormal subdistributions, which possibly represent different preferred rupture initiation points rather than a uniform distribution of initiation points. The event term subdistributions with highest median values have small standard deviations, so if shapes of this nature were used in ground‐motion prediction equations (GMPEs) during a probabilistic seismic‐hazard analysis, the effect of the long tail of the lognormal distribution in controlling the hazard would be weakened considerably. Static stress drop was recorded for each event, and event terms for PGA and PGV are well correlated with static stress drop. Unlike Next Generation Attenuation‐West 2 GMPEs, residual variances for the foam model are dominated by variability in the source slip function, rather than the path and site effects. This difference in the variance budget results from the way in which the source and site residuals are defined in this study; the source uncertainty includes variation in the rupture size (magnitude) and location, along with deviations in distance and path. We do not know if these results apply to earthquakes, but we do think tests of repeating stick‐slip events in a physical system are useful to expand the set of credible hypotheses regarding possible behavior modes of earthquake faults.