Three groups of single‐crystal disks approximately 5‐mm thick with surface normals along [100], [110], and [111] crystallographic directions were prepared from 99.99+ at.% pure copper. These specimens were shock loaded to about 50 kbar in a state of uniaxial strain by nitroguanidine explosive plane‐wave generators, and the propagated wave profiles were measured with quartz gauges. Elastic wavefronts for the single crystals exhibited sharp risetimes (of the order of 10 nsec) to dynamic yield points, and subsequent stress relaxations preceding the plastic wavefronts. For the propagation distances of about 5 mm, the measured yield point normal stresses were about 2.0, 1.3, and 1.3 kbar, respectively, for wave propagation in the [100], [110], and [111] directions. Although the principal stress states at the yield points differed, analysis reveals that the shear stresses on {111} ⟨110⟩ slip systems were about the same for all orientations. Single‐crystal disks prestrained by about 3½% exhibited essentially zero yield stresses and ramp‐like elastic waves. Similar behavior observed for polycrystalline specimens indicates the importance of initial dislocation density on dynamic yielding. In all cases the plastic wave velocities were the same. Constitutive relations derived on the basis of dislocation dynamics are given for the three single crystal orientations. From these relations the decay of the respective dynamic yield points with increasing propagation distance can be predicted as a function of the dislocation mobility and the initial mobile dislocation density. Within the framework of this theory it is shown that simple dislocation damping models for the mobility are not consistent with the experimental results.