We investigate the inertia-driven breakup of viscous drops suspended in a less viscous liquid under simple shear. For Stokes flow, it is known that there is a critical value of the viscosity ratio, beyond which breakup does not occur. We find that for viscosity ratios larger than this, inertia can be used as a mechanism of breakup. Inertia increases the angle of tilt of the drops and effectively leads to emulsification for a wider range of viscosity ratios than in Stokes flow. (C) 2003 American Institute of Physics.