We studied the motion of polycrystalline solids comprising of charged sub-micron latex spheres suspended in deionized water. These were subjected to a low frequency alternating square wave electric field in an optical cell of rectangular cross section. Velocity profiles in X and Y direction were determined by Laser Doppler Velocimetry. The observed complex flow profiles are time dependent due to the combined effects of electro-osmosis, electrophoresis, crystal elasticity, and friction of the crystals at the cell wall. On small time scales elastic deformation occurs. On long time scales channel formation is observed. At intermediate times steady state profiles are dominated by a solid plug of polycrystalline material moving in the cell center. At large field strengths the plug shear melts. Mobilities in the shear molten state are on the order of (6.5+/-0.5) 10(-8) m(2) V-1 s(-1) and connect continuously with those of the equilibrium fluid. The apparent mobility of the plug is much larger than of the fluid and like the mobility of the fluid decreases with increasing particle number density. We qualitatively attribute the accelerated motion of the plug to an incomplete exposure to the electro-osmotic flow profile. (C) 2003 American Institute of Physics.