Through molecular dynamics, the sliding motion of a liquid drop embedded in another liquid over a substrate as a result of a shear flow is studied. The two immiscible Lennard-Jones liquids have the same density and viscosity. The system is isothermal. Viscosity, surface tension, and static contact angles follow from calibration simulations. Sliding speeds and drop deformations (in terms of dynamic contact angles) are determined as a function of the shear rate. The latter is nondimensionalized as a capillary number (Ca) that has been varied in the range 0.02-0.64. For Ca up to 0.32, sliding speeds are approximately linear in Ca. For larger Ca, very strong droplet deformations are observed. (c) 2015 American Institute of Chemical Engineers.