We describe a methodology for generating kinematic earthquake ruptures for use in 3D ground‐motion simulations over the 0–5 Hz frequency band. Our approach begins by specifying a spatially random slip distribution that has a roughly wavenumber‐squared fall‐off. Given a hypocenter, the rupture speed is specified to average about 75%–80% of the local shear wavespeed and the prescribed slip‐rate function has a Kostrov‐like shape with a fault‐averaged rise time that scales self‐similarly with the seismic moment. Both the rupture time and rise time include significant local perturbations across the fault surface specified by spatially random fields that are partially correlated with the underlying slip distribution. We represent velocity‐strengthening fault zones in the shallow (<5  km) and deep (>15  km) crust by decreasing rupture speed and increasing rise time in these regions. Additional refinements to this approach include the incorporation of geometric perturbations to the fault surface, 3D stochastic correlated perturbations to the P‐ and S‐wave velocity structure, and a damage zone surrounding the shallow fault surface characterized by a 30% reduction in seismic velocity. We demonstrate the approach using a suite of simulations for a hypothetical M_w 6.45 strike‐slip earthquake embedded in a generalized hard‐rock velocity structure. The simulation results are compared with the median predictions from the 2014 Next Generation Attenuation‐West2 Project ground‐motion prediction equations and show very good agreement over the frequency band 0.1–5 Hz for distances out to 25 km from the fault. Additionally, the newly added features act to reduce the coherency of the radiated higher frequency (f>1  Hz) ground motions, and homogenize radiation‐pattern effects in this same bandwidth, which move the simulations closer to the statistical characteristics of observed motions as illustrated by comparison with recordings from the 1979 Imperial Valley earthquake.