Small angle neutron scattering (SANS) experiments were performed to examine the long range order in polymeric, micellar crystals subjected to linear steady shear. Polystyrene/polyisoprene (PS/PI) diblocks with varying degrees of polymerization and block asymmetry are used to generate both body-centered (BCC) and face-centered (FCC) cubic micellar crystals when suspended in decane. The FCC crystals show a transition from polycrystallinity to [111] sliding layers. This transition is marked by a significant hysteresis in the steady shear stress versus shear rate data. For higher shear rates, we observe [111] layers normal to the shear gradient slipping past each other. As the shear rate increases, the layers do not hop perfectly from one registry site to the next. The BCC crystals subjected to linear shear demonstrate a more continuous deformation of the local crystalline lattice that eventually develops into a BCC twin structure with the [110] layers normal to the shear gradient. The BCC twins advance in portions along the twinning planes, allowing the crystal to flow at moderate shear rates. At higher shear rates we observe a loss of long range order associated with shear melting. These results show an interesting similarity to other cubic crystals observed in both colloids and diblock melts.