The deformation of a liquid drop with constant isotropic surface tension and finite surface viscosity, evolving under the action of a simple shearing flow, is considered. The evolution of the drop from the spherical shape is computed using a novel implementation of the boundary integral method that incorporates the effects of interfacial rheology in an efficient manner. The numerical results confirm that surface viscosity acts to suppress the interfacial motion and reduce the magnitude of drop deformation. When the surface viscosity is sufficiently large, the drops maintain a compact shape at all capillary numbers. The effect of surface viscosity on the rheology of a dilute emulsion is considered, and it is found that, in all cases, a dilute emulsion behaves like a shear-thinning medium with some elastic properties.