<p>The flow of a drop in simple shear flow is studied in two- and three-dimensions including inertia effects. The Navier–Stokes equations are solved by a finite difference/ front tracking method. The lower and upper walls are moving with a constant velocity in opposite directions, and the simulation parameters are chosen to ensure that droplet breakup does not occur. It is found that drop migrates towards the centerline, and steady state position of the drop is on the channel centerline. The steady state position of the drop is always at the center line for all the flow parameters including the viscosity ratio and the Weber number at low and moderate Reynolds numbers. At relatively high Reynolds numbers (100) the drop attains oscillatory motion with a specific period for a two-dimensional drop. The same behavior is observed in three dimensions at higher density and viscosity ratios (150), and relatively low Reynolds numbers (10). The map of drop velocity and deformation with respect to its lateral position shows a single orbit after an initial transition period. In other words, the drop dynamics reach a stable limit cycle when the drop lateral position is used to parametrize in phase space. The drop deformation affects the lateral migration in the transient stage, i.e. the drop migrates faster to the centerline when the deformation is larger. However, the steady state position is not affected by the drop deformation.</p>